Triangle A B C is shown. Angle A C B is a right angle, angle C A B is 60 degrees, and angle A B C is 30 degrees. The length of the hypotenuse is 10. What are the lengths of the …

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asked Jun 11, 2021 30.3k views

2 Answers

Sam Casil · Answer 1 · 2021-06-15T10:41:51+0000

Answer : The lengths of the other two sides of the triangle is, 5 and
5√(3)

Step-by-step explanation :

Given:

∠ACB = 90°

∠CAB = 60°

∠ABC = 30°

Length of hypotenuse = 10

According to trigonometric function,

$\sin \theta=(Perpendicular)/(Hypotenuse)$

First we have to calculate the length AC.

$\sin 30^o=(Perpendicular)/(Hypotenuse)$

$\sin 30^o=(AC)/(AB)$

As we know that,
$\sin 30^o=(1)/(2)$

(1)/(2)=(AC)/(10)

AC=5

Now we have to calculate the length CB.

$\sin 60^o=(Perpendicular)/(Hypotenuse)$

$\sin 60^o=(CB)/(AB)$

As we know that,
$\sin 60^o=(√(3))/(2)$

(√(3))/(2)=(CB)/(10)

CB=5√(3)

Therefore, the lengths of the other two sides of the triangle is, 5 and
5√(3)