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.
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°
