Math Analysis
UNIT TT
TRIANGLE TRIGONOMETRY
REVIEW PROBLEMS
I.
Geometric Applications
1)
Find the area of a decagon inscribed in a circle with a radius of 11 inches.
2)
Find the measure for the included angle of a triangle that is created by sides with
lengths of 36 and 10 units and has an area of 24 square units.
3)
Find the lengths of the diagonals of an isosceles trapezoid if the bases of the
trapezoid are 22 cm and 10 cm and the height of the trapezoid is 3 cm.
4)
Find the area of the parallelogram
shown.
5)
Find the length of the diagonals of the
parallelogram shown.
15
112
23
18
11
37
6)
Find the area of the quadrilateral
shown.
17
6
118
90
9
MPH/CR 10/08
7)
Find the area of the quadrilateral
shown.
15
8
100
115
10
1
Math Analysis
II.
Right Triangle Trigonometry
1)
The sides of an isosceles triangle are 5, 10, and 10. Find the measures of its angles.
2)
At a distance of 100 m, the angle of elevation to the top of a fir tree is 28. How
tall is the tree?
3)
If tan  = 7/6, find the remaining five remaining trigonometric ratios for . Give
exact answers.
4)
A ladder leaning against a house makes a 17 angle with the ground. If the ladder is
20 feet long, what is the distance from the base of the ladder to the house?
5)
A sonar operator on a cruiser detects a submarine at distance of 500 m and an angle
of depression of 37. How deep is the submarine?
III. The Ambiguous Case
Determine the number of solutions for each of the triangles shown. Do not solve the
triangles.
1)
mC = 55, a = 11, c = 18
2)
mA = 63, a = 3, b = 8
3)
a = 5, b = 4, mB = 74
4)
mC = 52, b = 8, c = 7
5)
a = 9, c = 8, mA = 23
IV.
Solving the Triangle
Solve each of the following triangles.
1)
mR = 75, mS = 45, t = 3
2)
mA = 100, mC = 30, c = 8
3)
a = 17, b = 10, c = 21
4)
q = 6, r = 7, mP = 50
5)
mX = 21.1, x = 6, y = 9
6)
a = 10, b = 11, c = 12
7)
mM = 11, n = 15, p = 6
MPH/CR 10/08
2