Question

Determine the unknown length or angle measurement. Round each answer to the nearest whole number

Answer 1

Θ ≈ 37° , x ≈ 13 cm

Explanation:

(a)

using the cosine ratio in the right triangle

cosΘ =
`(adjacent)/(hypotenuse)` =
`(BC)/(AC)` =
`(8)/(10)` , then

Θ =
`cos^(-1)` (
`(8)/(10)` ) ≈ 37° ( to the nearest whole number )

(b)

using the sine ratio in the right triangle and the exact value

sin60° =
`(√(3) )/(2)` , then

sin60° =
`(opposite)/(hypotenuse)` =
`(x)/(15)` =
`(√(3) )/(2)` ( cross- multiply )

2x = 15
`√(3)` ( divide both sides by 2 )

x = 7.5
`√(3)` ≈ 13 cm ( to the nearest whole number )