Find the value t of ∆TUV where ∠T = 54°, ∠U = 67°, and u = 14.
Hint
The letter of the angle relates to the letter of the side. Using that and the Law of Sines, we should be good to go.
Answer
t ≈ 12.3
Example 2
Find the value of x.
Hint
The angles of a triangle always add up to 180°.
Answer
x ≈ 7
Example 3
Find the value of x.
Hint
Law of Sines, all the way.
Answer
x ≈ 51.9
Example 4
Will, Bill, and Steve are playing baseball. Will, the pitcher, stands 60.5 ft away from Bill at home plate and 50 ft away from first base, where Steve is tying his shoe. If home plate is the vertex of a 44° angle between first base and the pitcher's mound, how far away are Bill and Steve, approximately?
Hint
Drawing this out might help. The angle and side ratio that goes together is the 44° angle at home and the 50 ft between Will and Steve. Finding all the angles is the best way to get to the answer.
Answer
Bill and Steve are about 70.6 ft apart.
Example 5
A spaceship has traveled some distance away from its home planet, Zargon, along a straight path. Alluron, a nearby star, is behind the spaceship at an angle of 32°. Zargon is the vertex of a 73° angle between Alluron and the spaceship, and Zargon and Alluron are known to be 25 million light-years away from each other. How far has the spaceship traveled, in light-years?
Hint
The spaceship, Zargon, and Alluron are three points of a triangle. If we abbreviate them S, Z, and A, we have ZA = 25, ∠AZS = 73°, and ∠ZSA = 32°. We have to find SZ.
Answer
The spaceship is about 45.6 million light-years away from Zargon.
Example 6
The roof of a house makes an isosceles triangle with a vertex of 50°. If each side of the roof is 18 feet long, how wide is the house?
Hint
The triangle is isosceles, which means that the two remaining angles must be equal to each other.
