Download Practice Test Lesson 1 Unit 7 Name_____________________

Practice Test Lesson 1 Unit 7
Name_____________________
Please, if necessary, round all answers to the nearest hundredth.
1. Consider the line that contains the origin and the point with coordinates ( 7, 24).
a. Sketch this line and find the equation of the line.
b. Label the angle formed by the line and the positive x-axis . Without using your calculator, express the
following in ratio form.
tan  =
cos  =
sin  =
2. Triangle ACB is a right triangle with side BC = 6 and hypotenuse AB = 10.
a. Compute the length of side AC.
b. Without using your calculator, find the following. Express your answers in ratio form.
tan A =
cos A =
3. Solve the triangle. Show all of your work.
sin A =
4. Usually, it is not possible to measure the heights of very tall structures, like towers or flagpoles,
with a tape measure. Surveyors use right triangle trigonometry, measuring lengths that are accessible
with a tape measure (or other tool) and angles between two lines of sight with a transit. Rita uses the
transit, which is 3.6 m high and 28 m from the flagpole (on level ground), to sight to the top of the
flagpole. The angle of elevation to the top of the flagpole measures 68°. Label these measures on the
sketch below.
a. Find the height of the flagpole to the nearest tenth of a meter. Show your work.
a. How far is it from the transit to the top of the flagpole? Show your work.
5. James needs to attach a stabilizing wire to a tall tower. The wire is 400 feet long and should be
attached to the tower at a height of 300 feet. Assume that the ground around the tower is level and
that the entire length of the wire is used.
a. Draw a sketch of this situation and label any known lengths.
b. Determine the angle that the wire will make with the ground.
c. Find the distance from the tower to the point where the wire is attached to the ground.
6. Alisha is standing on one side of a canyon, and her friend Alex is standing directly across the
canyon from her on the other side. They want to know how wide the canyon is. Alisha marks her spot
and then walks 25 yards along the canyon edge and looks back at Alex. The angle of her line of sight to
Alex and the path she just walked is 68°.
a. Draw a sketch that illustrates this situation. and find the width of the canyon. Show all of your work.
7. Demetri leans a 35-ft ladder against a wall. The base of the ladder is 5 feet from the wall.
a.
What angle does the ladder make with the ground? Show your work.
b.
How high up the wall does the ladder reach? Show your work.
1.
A table can be tilted forward to make working on architect drawings easier
a)
2.
Suppose the sides that make the right angle, AB = 12 inches and BC = 10 inches
i.
What is the measure of angle BAC?
ii
What is the length of side AC?
You are standing 25 feet away from a tree, and you measure the angle of elevation (from
your eyes which are 5 feet off the ground) to be 35°. How tall is the tree?