Question

What is the measure of ∠w, rounded to the nearest degree? 19° 19° 32° 32° 56° 56° 71° 71° a horizontally-aligned scalene triangle u v w. side u v is labeled as 35 meters. side v w is labeled as 30 meters. side u w is labeled as 30 meters.

Answer 1

(d) 71°

Explanation:

The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.

Sine

Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.

sin(W/2) = Opposite/Hypotenuse

sin(W/2) = (35/2)/(30) = 7/12

Using the inverse sine function, we find ...

W/2 = arcsin(7/12) ≈ 35.685°

W = 2×36.684° = 71.37°

W ≈ 71°

Law of cosines

The law of cosines tells you ...

w² = u² +v² -2uv·cos(W)

Solving for W gives ...

W = arccos((u² +v² -w²)/(2uv))

W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°

W ≈ 71°