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Simora [160]
1 year ago
13

What is the measure of ∠w, rounded to the nearest degree? 19° 19° 32° 32° 56° 56° 71° 71° a horizontally-aligned scalene triangl

e 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.
Mathematics
1 answer:
ella [17]1 year ago
7 0

Answer:

  (d)  71°

Step-by-step 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.

<h3>Sine</h3>

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°

<h3>Law of cosines</h3>

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°

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