5-2 Applications of Right Triangle Trigonometry Download

Transcript
Math 2
Lesson 5-2: Applications of Right Triangle Trigonometry
Name ______________________________
Date __________________________
Learning Goals:
 I can solve right triangles by finding the measures of all sides and angles in the triangles.
 I can use sine, cosine, tangent, and their inverses to solve for the unknown side lengths and angle
measures of a right triangle.
 I can draw right triangles that describe real world problems and label the sides and angles with
their given measures.
 I can solve application problems involving right triangles, including angle of elevation and
depression, navigation and surveying.
1. The diagram below shows Ralph’s attempt to determine the height of Top Thrill Dragster without
climbing to the top of the ride & dropping a tape measure down to the ground. He measured his
distance from the base of the ride and found that he was 185.5 feet away. Next, he used a clinometer
app on his Smartphone to measure the angle of elevation, which came out to be 66.5°.
a. Label the diagram below with the measurements
Ralph came up with.
b. Using that information and trigonometry,
calculate the height of Top Thrill Dragster.
Round to the nearest foot.
2. Many times when solving trigonometric word problems, you must draw and label a sketch of the
scenario. You will either be given the angle of elevation or the angle of depression. Sometimes you
might even have to calculate the angle. IT IS VERY IMPORTANT THAT YOU PLACE THE ANGLE
MEASURE IN THE RIGHT SPOT IN YOUR DIAGRAM.
Here are a couple of pointers:
o Angle of elevation and angle of depression are the angle made with the horizontal line.
o The horizontal line intersects the starting point, and the other (sloped) line intersects the
ending point.
o The angles of depression and elevation are always ________________, since they are really
______________________________________.
OVER 
3. Use the diagram below to match angles with their descriptions:
angle of depression from boat to submarine ______
angle of depression from lighthouse to boat ______
angle of depression from the waterfall to Kelley ______
angle of depression from the waterfall to Jim ______
angle of elevation from submarine to boat ______
angle of elevation from Kelley to the waterfall ______
angle of elevation from Jim to the waterfall ______
angle of elevation from boat to lighthouse ______
4.
B
ground
A
?
5.
B
Find the missing parts of the triangles. Round to the nearest 100th.
6.
7.
mA  90
AB  4.39cm
mB  _____
AC  ______
mC  _____
BC  5.94cm
Draw & label sketches for the following scenarios. Label and round your answers to the nearest 100th.
8. The lift hill of Cedar Point’s Millennium Force rises at an angle of 45. The height at the top of the first
hill is 310’. How long is the track from the base of the lift hill to its top?
9. The Mardi Gras Xpress ski lift at Holiday Valley is 4400 feet long. The vertical distance from the base
of the mountain to the top of the lift is 2250 feet. What is the angle of elevation?
Lesson 5-2 Homework
***Round all answers to the nearest 100th.
A.)
B.) A 20 ft ladder forms an angle θ of
40° with the ground when placed
against a brick wall. How far is the
base of the ladder from the wall?
On another sheet of paper, draw & label diagrams for each of the
problems listed below.
Round all answers to the nearest 100th.
Label your answers with the appropriate units.
1. From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree is
64.3o. Find the height of the tree to the nearest foot.
2. DME (Distance Measuring Equipment) is standard avionic equipment on a commercial airplane. This
equipment measures the distance from a plane to a radar station. If the distance from a plane to a radar
station is 160 miles and the angle of depression is 33o, find the number of ground miles from a point
directly below the plane to the radar station.
3. The angle of elevation from a point 116 meters from the base of the Eiffel Tower to the top of the Tower
is 68.9o. Find the approximate height of the tower.
4. A submarine is descending at an angle of depression of 5o. How far has it traveled when it reaches a
depth of 80 feet?
5. The angle of depression of one side of a lake, measured from a balloon 2500 feet directly above the lake
is 43o. The angle of depression to the opposite side of the lake is 27o. Find the width of the lake.
6. The first hill of Cedar Point’s Maverick is 105 feet high. Find the length of the lift hill if its angle of
elevation is 29.5°.
7. An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists are
driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 35°
and to the other is 52°. How far apart are the cars?
8. A 50 foot pole casts a shadow of 42 feet. At that particular moment, find the angle of elevation of the
sun.
9. Ralph is flying a kite. The string of the kite makes an angle of 30 degrees with the ground. If the height
of the kite is 24m above the ground, find the length of the string that is being used by the boy. Assume
that the string is taut.
10. A 5.2 meter ladder leans against a wall. The bottom of the ladder is 1.9 meters from the wall. What
angle does the ladder make with the ground?
11. Two people on opposite sides of a tower of height 150 meters notice the angle of elevation to be 39°
and 64° respectively (the people are on the sidewalk looking up at the tower) . The tower is 28 meters
wide. Find the distance between the two people.
12. The tailgate of a truck is 3.5 feet above the ground. The incline of a ramp used for loading the truck is
15◦. Find the length of the ramp.