Solve the Triangle
Missing Lengths
Inverse Trig
Bearings
Elevation/Depression
100
What is AC (round to the nearest hundredth) if AB = 9 and angle C = 20o?
26.13
100
What is the value for x? Round to the nearest hundredth.
61.82
100
What is the angle? Round to the nearest hundredth.
32.02o
100
A taxi travels through 5 city blocks west and then 8 blocks north. Assuming all city blocks are the same distance apart, what is the heading (measuring from due north) of the new location from the original spot? Round to the nearest degree.
328o (N32oW)
100
Find the shadow cast by a 10-foot lamp post when the angle of elevation of the sun is 58º. Round the answer to the nearest hundredth.
6.25 feet
200
What is the measure of angle C (round to the nearest hundredth) if AB = 8, BC = 15, and AC = 17?
28.07 degrees
200
What is the value for x? Round to the nearest hundredth.
5.34
200
What is the angle? Round to the nearest hundredth.
34.82o
200
A plane flew from Baltimore 110 miles with the bearings of S24oW. How far south did the plane traveled? Round the answer to the nearest miles.
100 miles
200
From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40o. If the tower is 45 feet in height, how far is the partner from the base of the tower? Round to the nearest hundredth.
53.63 feet
300
What is AB (round to the nearest hundredth) if angle A is 52o and the hypotenuse is 50 feet?
30.78 feet
300
What is the value for x? Round to the nearest hundredth.
41.06
300
What is the angle? Round to the nearest hundredth.
56.44o
300
Runway 19 at an airport means that the runway has a heading of 190o, which means the plane is flying S10oW. What is the bearing of Runway 30?
N60oW
300
If a man is just about to ski down a steep mountain. He estimates the angle of depression from where he is now to the flag at the bottom of the course to be 24°. He knows that he is 800 feet higher than the base of the course. How long is the path that he will ski? Round to the nearest hundredth.
1966.87 ft
400
What is the measure of angle A (round to the nearest hundredth) if BC = 17 and AC = 28?
37.38o
400
What is the horizontal distance the hiker walked? Round to the nearest hundredth.
9.40 miles
400
A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall? Round the answer to the nearest hundredth.
68.21o
400
To avoid a hurricane, a cruise ship detoured and traveled 45 miles south and then 32 miles east. What is the bearing of the current location from the original spot?
S35oE (145o)
400
Adrian is flying a kite. He is holding the end of the string at a distance of 1.5 m above the ground. If the string is 20 m long and makes an angle of 40° with the horizontal, how high is the kite above the ground? Round to the nearest hundredth.
14.36 meters
500
What is BC if AB = 8 and AC = 16? Round to the nearest hundredth.
13.86
500
What is the height of the flag pole? Round to the nearest hundredth.
51.20 feet
500
An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building? Round the answer to the nearest hundredth.
(1 yard = 3 feet)
5.71o
500
You walked .5 miles south, .3 miles west, and then another .2 miles south to get to Whole Food. But you ordered drone delivery the food back to the house. How far would the drone travel if it flew in a straight line from the store to your house? Round to the nearest hundredth.
0.76 mile
500
Obiwan is standing at a distance of 15 m from the base of a tree. From where he is standing, he can see the top of the tree. If the tree is 15 m high and Obiwan is 1 m tall, what is the angle of elevation of the top of the tree? Round to the nearest hundredth degree.
43.03o