Question

Quick!!! Solve for the missing lengths using trigonometric ratios.

*
110m
42°
Х

Answer 1

see explanation

Explanation:

using the tangent ratio in the right triangle to find x

tan42° =
`(opposite)/(adjacent)` =
`(10)/(x)` ( multiply both sides by x )

x × tan42° = 10 ( divide both sides by tan42° )

x =
`(10)/(tan42)` ≈ 11.1 ( to 1 dec. place )

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using the sine ratio to find the hypotenuse h

sin42° =
`(opposite)/(hypotenuse)` =
`(10)/(h)` ( multiply both sides by h )

h × sin42° = 10 ( divide both sides by sin42° )

h =
`(10)/(sin42)` ≈ 14.9 ( to 1 dec. place )