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(Answer) MATH114N – Week 6 Assignment: Triangles and the Pythagorean Theorem

Question 1

One angle of a right triangle measures 36.5 degrees. What is the measure of the other small angle?

Question 2

One side of a triangle is 2 times the second side. The third side is 5 feet longer than the second side. The perimeter of a triangle is 81 feet. Find the length of each side.

Question 3

Brian borrowed a 20 foot extension ladder to use when he paints his house. If he sets the base of the ladder 6 feet from the house, as shown below, how far up will the top of the ladder reach? Round to one decimal place.

A house is shown with a ladder leaning against it. The ladder is marked 20’, and the distance from the house to the base of the ladder is marked 6’.

Question 4

Chi is planning to put a path of paving stones through her flower garden, as shown below. The flower garden is a square with a side length of 10 feet. What will be the length of the path? Round your answer to 2 decimal places.

A square garden is shown that is marked 10’ on the side. There is a path of stones along the diagonal of the square.

Question 5

If a triangle has side lengths of 14 centimeters and 18 centimeters and the perimeter is 49 centimeters, how long is the third side?

Question 6

The perimeter of a triangle is 82 feet. One side of the triangle is 2 times the second side. The third side is 2 feet longer than the second side. Find the length of each side.

Question 7:

What is the height of a triangle with an area of 67.5 square meters and a base of 9 meters?

Question 8:

One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?

Question 9

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

The figure shows a right triangle with one leg marked 20. The hypotenuse is marked 25.

Question 10

Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.

Question 11

The measure of one angle of a right triangle is 38∘ more than the measure of the smallest angle. Find the measures of all three angles.

Question 12

In a right triangle, the measure of one of the acute angles is 60 degrees more than the measure of the smallest angle. Find the measures of all three angles.

ANSWERS:

Question 1

One angle of a right triangle measures 36.5 degrees. What is the measure of the other small angle?

Answer: 53.5 degrees

Question 2

One side of a triangle is 2 times the second side. The third side is 5 feet longer than the second side. The perimeter of a triangle is 81 feet. Find the length of each side.

Answer: 38 feet, 19 feet, 24 feet

Question 3….

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