Right Triangles

111.8 yards

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

150 meters

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run?

95√2

A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

22.21 m

A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42°. Calculate the distance, in m, of the ball from the base of the tower.

45 feet

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse?

16.70 degrees

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?HINT: Assume this is a right triangle.

40 miles

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

cos(37)=x/14

Choose the correct ratio.

Obtuse

Classify the triangle as obtuse, acute, or right Side lengths: 15, 8, and 12

Acute

Do these three lengths form a right, acute or obtuse triangle? 20 ft, 21 ft, and 27 ft

2√3

Find n.

288

Find the area of the missing square off of leg A if the area of one square is 369 and the area of another is 81?

89.6

Find the area of this triangle. Round your answer to the nearest tenth.

18.0

Find the length of side w.

76.34

Find the length of side y.

13

Find the length of the missing side.

48

Find the length of the missing side.

52

Find the length of the missing side.

55.2 degrees

Find the measure of the indicated angle (?) round to the nearest tenth.

26 degrees

Find the measure of the missing angle.

7√3

Find the value of y.

8

Find the value of y.

9√2

Find the value of y.

220.80 meters

From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33°. Find the height of the dam to the nearest meter.

Divide 6 by 2

I have been given the hypotenuse in this 30-60-90 triangle. How do I find the short leg?

Divide 7 by √3

I have been given the long leg in this 30-60-90 triangle. How do I find the short leg?

14.4 ft

In the Old West, settlers made tents out of a piece of cloth thrown over a clothesline and then secured it to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide?

19 degrees

Jake built a skateboard ramp that covers a horizontal distance of 10 ft. The ramp rises a total of 3.5 ft. What angle does the ramp make with the ground? Round to the nearest degree.

cos X = 28/41

Set up the problem...

a = 5√2, b = 5√2

Solve for a and b in the special right triangle.

36.9 degrees

Solve for the missing angle.

y = 4, x = 4√3

Solve for x and y in the special right triangle.

87 ft

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

12 ft

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

7.44

What is the length of side x?

u = 8 v = 4√3

What is the length of u and v in this 30-60-90 triangle?

right

What kind of triangle do the segment lengths 15, 12, and 9 form?

∠Z = cos^(-1) 55/73

Which of the following is correct for finding the measure of angle Z?

16√3

You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? (hint: use 30-60-90 theorems)

13.7 inches

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

127.3 feet

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

30 ft

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?