Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
State your answers in simplest form. (simplest radical form)
1. 2.
Tell whether the triangle is a right triangle.
3. 4.
Verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse?
5. 6.5, 7, and 8
7.A ski lift forms a right triangle, as shown. Use the Pythagorean Theorem to approximate the horizontal distance traveled by a person riding the ski lift. Round your answer to the nearest whole foot.
Complete the tables. Write your answers in simplest form.
1. 2.
Find the values of the variables. Write your answers in simplest form.
3. 4. 5.
Find the area of the figure. Round decimal answers to the nearest tenth. (do not round until stating your answer)
6. 7.
Find the value of x.
1.
Find the geometric mean of the two numbers. State your answer in simplest form.
2. 3 and 12 3.4 and 14
find the value of x.
4. 5. 6.
7. You are designing a diamond-shaped kite. You know that You want to use a straight
crossbar About how long should it be?
Find the value of x. Round your answer to the nearest tenth.
1. 2. 3.
4. 5. 6.
7. You are measuring the height of a water slide. You stand 58 meters from the base of the slide. You measure the angle of elevation from the ground to the top of the water slide to be Find the height h of the slide to the nearest meter.
Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
1. 2. 3.
4. The angle of depression is from the bottom of a boat to a deep sea diver at
a depth of 120 feet.Find the distance x the diver must swim up to the boat to the nearest foot.
5. You use an extension ladder to repair a chimney that is 33 feet tall. The length of the extension ladder ranges in one-foot increments from its minimum length to its maximum length. For safety reasons, you should always use an angle of about between the ground
and your ladder.
a.Your smallest extension ladder has maximum length of 17 feet. How high does this ladder safely reach on the chimney? Round your answer to the nearest tenth of a foot.
b.You place the ladder 3 feet from the base of the chimney. How many feet long should the ladder be? Round your answer to the nearest foot.
c.To reach the top of the chimney, you need a ladder that reaches 30 feet high. How many feet long should the ladder be? Round your answer to the nearest foot.
Solve the right triangle. Round decimal answers to the nearest tenth. State lengths in simplest form if using the PythagoreanTheorem.
1. 2.
3. Use the diagram to find the distance across the suspension bridge. Round your answer to the nearest foot.
4. Use the diagram to find the acute angle formed by
Washington Boulevard and Willow Way. Round
your answer to the nearest tenth.
5. You are in a hot air balloon that is 600 feet above the ground. You can
see two people. The angles of depression to person B and to person C
are and respectively.
a. How far is person B from the point on the ground below the hot air balloon?
b. How far is person C from the point on the ground below the hot air balloon?
c. How far apart are the two people?