Download Mixed Trig Review

Geometry – accel.
Mixed Trig Review Problems
April. 18, 2013
Remember to check that your calculator is in degrees mode! Round lengths and areas to
nearest hundredth, degrees to nearest tenth.
Solve the following triangles where possible (find all missing sides and angles).
1. a = 8, b = 7, c = 12
2. b = 1.61, c = 2.08, A = 51º
B
3. a = 10, b = 13, Area = 65
4. b = 18, c = 7, Area = 65
5. B = 49º, C = 41º, c = 22
6. A = 19º, a = 25, b = 30
7. a = 130, A = 39º, B = 65º
a
c
* not to scale *
A
b
C
8. A = 126º, a = 5, b = 7
9. A = 58º, a = 9.3, c = 7.5
10. A = 28º, a = 50, b = 20
11. The sides of a triangular lot are 32, 48 and 28 meters in length. Find the
area of the lot and the measure of the largest angle.
12. The area of ABC is 21.213 square feet; AC = 5 ft., and angle C = 45º. Find
the length of BC and the length of the altitude to BC.
13. If the measures of two angles are equal, then the sides opposite these
angles must be congruent. Prove this using the Law of Sines.
14. Two adjacent sides of a parallelogram are 15 and 24 and have an included
angle of 50º. Find the lengths of both diagonals and the acute angle at which
they intersect. Find the area of the parallelogram and the distances between the
parallels.
15. In an isosceles triangle, the length of the base is 30 cm, and the vertex angle
is 50º. Find the length of the legs, the lengths of the altitudes, and the area of
the triangle.
16. The diagonals of a parallelogram have lengths of 6 and 10 and intersect at a
33º angle. Find the lengths of the sides of the parallelogram.
17. A tall evergreen tree has been damaged by a strong wind. The top of the
trunk is cracked and bent over, touching the ground as if the trunk were hinged.
The tip of the tree touches the ground 20.5 feet from the base of the tree and
makes a 38º angle with the ground. Determine the original height of the tree, to
the nearest foot.
18. A lighthouse is due east of a Coast Guard patrol boat. The Coast Guard
station is 20 km north of the lighthouse. The radar officer aboard the ship
measures the angle between the lighthouse and the station to be 23º. To the
nearest kilometer, how far is the ship from the station?
19. A tree is growing vertically on a hillside that is slanted at 16º from horizontal.
The tree casts a shadow 55 feet long going uphill from the base of the tree. If the
angle of elevation of the sun is 68º, how tall is the tree?