Question

Find the value of x for the triangle below.

Answer 1

Explanation:

in the given triangle . one angle is 90 degree and other angle = 30

therefore third angle = 180 - 120 ( angle sum property of a triangle)

third angle = 60 degree

sin 30 = 5 / x (1)

cos 30 =third side /x (2)

from 1 * 2 we get ,

SIN 30 * COS 30 = 5/X * THIRD SIDE / X

1/2 *
`√(3)`/2 = 5 * THIRD SIDE / X^2

`√(3)` * X^2/10 = THIRD SIDE

BY APPLYING PYTHAGORUS THEOREM

X^2 = 5^2 + [
`√(3)` * X^2/10]^2

X^2 = 25 + 3x^4/100

x = square root of 25 + 3x^4/100 = 5+
`√(3)`x^2/10

x= 5+
`√(3)` * x^2/10

Answer 2

x = 10

Explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite/ hypotenuse

sin 30 = 5/x

Multiply each side by x

x sin 30 = 5

Divide by sin 30

x = 5/sin 30

x = 10