Question

Use a sine or cosine ratio to find the value of each variable. Round decimals to the nearest tenth.

Answer 1

a ≈ 14.9 , b ≈ 11.1

Explanation:

using the cosine ratio in the right triangle

cos48° =
`(adjacent)/(hypotenuse)` =
`(10)/(a)` ( multiply both sides by a )

a × cos48° = 10 ( divide both sides by cos48° )

a =
`(10)/(cos48)` ≈ 14.9 ( to the nearest tenth )

now use the sine ratio in the right triangle to find b

sin48° =
`(opposite)/(hypotenuse)` =
`(b)/(a)` =
`(b)/(14.9)` ( multiply both sides by 14.9 )

14.9 × sin48° = b , then

b ≈ 11.1 ( to the nearest tenth )