Question

Find the lengths of sides marked with variables (x, y, w, z). Show all work

Answer 1

#1

• sin27=x/42
• x=42sin27
• x=19.07m

#2

• tan23=34/x
• x=34/tan23
• x=80.1ft

#3

• cos48=38/x
• x=38/cos48
• x=56.79m

Answer 2

• 1) 19.07 m, 2) 80.10 ft, 3) 56.79 m

Explanation:

Use trigonometry to solve for unknowns.

1) Use sine

• sine = opposite leg / hypotenuse

• sin 27° = x/42
• x = 42 sin 27°
• x = 19.07 m (rounded)

2) Use tangent

• tangent = opposite leg / adjacent leg

• tan 23° = 34/x
• x = 34 / tan 23°
• x = 80.10 ft

3) Use cosine

• cosine = adjacent leg / hypotenuse

• cos 48° = 38/x
• x = 38 / cos 48°
• x = 56.79 m (rounded)