Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 5 Herrega kutaa 9: Seensa Tirigoonomeetirii

Wanti fuula kana irra jiru hundi boqonnaa 5 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

4
Kaardii: 10
Gaaffii shaakalaa boqonnaa 5: 162–180
Fuula kitaabaa boqonnaa 5

Boqonnaan 5 maal haguuga

1.Revision on Right-angled Triangles
2.The Trigonometric Ratios

Yaadannoo gabaabaa boqonnaa 5

Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Confusing Opposite and Adjacent SidesDogoggora baratame

Yoom akka itti fayyadamtu

Kofa qaraa kennameef reeshiyoo sine, cosine, yookiin tangent shallaguun dura kana ilaali.

Of eeggadhu

hypotenuse yeroo hunda kofa digrii 90 fuullee dhaabbataadha, garuu kofa qaraa tokkorraa gara isa biraatti yeroo jijjiirtu opposite fi adjacent bakka wal jijjiiru.

Grade 9 Mathematics, fuula 162-180 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Pythagoras TheoremFoormulaa

b^2 + p^2 = h^2

b^2 + p^2 = h^2

$h$: haayipoteniyuusii $m$
$b$: hundee $m$
$p$: cinaacha dhaabbataa $m$

Yoom akka itti fayyadamtu

Dheerina cinaacha rog-sadee kofa qajeelaa isa hin beekamne baruuf yookiin rog-sadeen sun kofa qajeelaa qabaachuu mirkaneessuuf itti fayyadami.

Of eeggadhu

hypotenuse h yeroo hunda cinaacha dheeraa fuullee kofa digrii 90 jiru ta'uu qaba. Bakka h cinaacha biraa hin galchin.

Grade 9 Mathematics, fuula 162-180 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Trigonometric RatiosFoormulaa

\sin A = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos A = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan A = \frac{\text{opposite}}{\text{adjacent}}

\sin A = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos A = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan A = \frac{\text{opposite}}{\text{adjacent}}

$A$: kofa qara $^\circ$
$\text{opposite}$: cinaacha kofa A'f fuullee ta'e $m$
$\text{adjacent}$: cinaacha kofa A maddii jiru $m$
$\text{hypotenuse}$: haayipoteniyuusii $m$

Yoom akka itti fayyadamtu

Rog-sadee kofa qajeelaa keessatti hariiroo kofa qaraa fi dheerina cinaachaa walbira qabuuf itti fayyadami.

Of eeggadhu

opposite fi adjacent kofa filatame irratti hundaa'u. Kofa A tiif cinaacha sirrii ta'uu isaa mirkaneessi.

Grade 9 Mathematics, fuula 162-180 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Trigonometric Values of Special AnglesGabatee wabiiA

Ratio	$0^\circ$	$30^\circ$	$45^\circ$	$60^\circ$	$90^\circ$
$\sin A$	$0$	$\frac{1}{2}$	$\frac{1}{\sqrt{2}}$	$\frac{\sqrt{3}}{2}$	$1$
$\cos A$	$1$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{2}}$	$\frac{1}{2}$	$0$
$\tan A$	$0$	$\frac{1}{\sqrt{3}}$	$1$	$\sqrt{3}$	undefined

Yoom akka itti fayyadamtu

Taabilee malee gatiiwwan kofoota beekamoo shallaguuf itti fayyadami.

Of eeggadhu

Gatiin tan digrii 90 zeeroof waan hiramuuf hiika hin qabu (undefined).

Grade 9 Mathematics, fuula 162-180 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 5

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

In a right-angled triangle, what is the special name given to the side opposite to the 90 degree angle?

A.Base
B.Perpendicular
C.Hypotenuse
D.Adjacent

Deebii fi sababa agarsiisi

Deebii: C Hypotenuse

Sababa

By definition, the side opposite to the right angle (90 degrees) in a right-angled triangle is called the hypotenuse, and it is always the longest side.

Gaaffii 2

What is the maximum degree measure of an interior angle in a right-angled triangle?

A.45 degrees
B.60 degrees
C.90 degrees
D.180 degrees

Deebii fi sababa agarsiisi

Deebii: C 90 degrees

Sababa

A right-angled triangle has one angle equal to 90 degrees, and the sum of the other two acute angles is 90 degrees. Therefore, the maximum interior angle measure is 90 degrees.

Gaaffii 3

The word trigonometry is derived from two Greek words: trigonon and metron. What does trigonon mean?

A.Measure
B.Triangle
C.Angle
D.Circle

Deebii fi sababa agarsiisi

Deebii: B Triangle

Sababa

According to the textbook, trigonon means triangle and metron means measure.

Gaaffii 4

For an acute angle A in a right-angled triangle, how is the tangent ratio (tan A) defined?

A.Opposite side divided by adjacent side
B.Adjacent side divided by hypotenuse
C.Opposite side divided by hypotenuse
D.Hypotenuse divided by adjacent side

Deebii fi sababa agarsiisi

Deebii: A Opposite side divided by adjacent side

Sababa

By definition, tan A = (side opposite to angle A) / (side adjacent to angle A).

Gaaffii 5

Which of the following sets of side lengths can form a right-angled triangle?

A.5, 6, 2
B.4, 6, 8
C.1, 2, √3
D.2, 3, 4

Deebii fi sababa agarsiisi

Deebii: C 1, 2, √3

Sababa

Using the converse of Pythagoras theorem: for side lengths 1, √3, and 2 (where 2 is the longest side), 1² + (√3)² = 1 + 3 = 4, and 2² = 4. Since LHS = RHS, these sides form a right-angled triangle.

Gaaffii 6

An equilateral triangle has sides of length 6 units. What is the height of this triangle?

A.3√3 units
B.3√2 units
C.2√5 units
D.3 units

Deebii fi sababa agarsiisi

Deebii: A 3√3 units

Sababa

Drawing a perpendicular height splits the base of 6 into two segments of 3 units each. By Pythagoras theorem, h² + 3² = 6², which gives h² + 9 = 36, so h² = 27, and h = 3√3 units.

Gaaffii 7

What is the exact value of tan 60°?

A.1 / √3
B.1
C.√3
D.√3 / 2

Deebii fi sababa agarsiisi

Deebii: C √3

Sababa

In a standard 30°-60°-90° right-angled triangle, the side opposite to 60° is √3 and the adjacent side is 1. Thus, tan 60° = √3 / 1 = √3.

Gaaffii 8

As the acute angle A increases from 0° to 90°, what happens to the values of sin A and cos A?

A.sin A increases from 0 to 1, while cos A decreases from 1 to 0
B.sin A decreases from 1 to 0, while cos A increases from 0 to 1
C.Both sin A and cos A increase from 0 to 1
D.Both sin A and cos A decrease from 1 to 0

Deebii fi sababa agarsiisi

Deebii: A sin A increases from 0 to 1, while cos A decreases from 1 to 0

Sababa

As noted in the textbook remark, as ∠A increases from 0° to 90°, sin A increases from 0 to 1 while cos A decreases from 1 to 0.

Gaaffii 9

In a right-angled triangle, if an acute angle A has sin A = 3/5, what is the value of tan A?

A.4/5
B.3/4
C.4/3
D.5/3

Deebii fi sababa agarsiisi

Deebii: B 3/4

Sababa

Since sin A = opposite / hypotenuse = 3/5, let opposite = 3 and hypotenuse = 5. By Pythagoras theorem, adjacent = √(5² - 3²) = √(25 - 9) = √16 = 4. Therefore, tan A = opposite / adjacent = 3/4.

Gaaffii 10

If A is an acute angle in a right-angled triangle and tan A = 1 / √2, what is the value of cos A?

A.1 / √3
B.√2 / √3
C.√3 / √2
D.1 / 2

Deebii fi sababa agarsiisi

Deebii: B √2 / √3

Sababa

With tan A = opposite / adjacent = 1 / √2, opposite = 1 and adjacent = √2. Hypotenuse = √(1² + (√2)²) = √(1 + 2) = √3. Therefore, cos A = adjacent / hypotenuse = √2 / √3.

Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.