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Solving Applications Using Triangle Properties
In the following exercises, solve using triangle properties.
The measures of two angles of a triangle are 26 and 98 degrees. Find the measure of the third angle.
56 degrees
The measures of two angles of a triangle are 61 and 84 degrees. Find the measure of the third angle.
The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.
44 degrees
The measures of two angles of a triangle are 47 and 72 degrees. Find the measure of the third angle.
The perimeter of a triangular pool is 36 yards. The lengths of two sides are 10 yards and 15 yards. How long is the third side?
11 feet
A triangular courtyard has perimeter 120 meters. The lengths of two sides are 30 meters and 50 meters. How long is the third side?
If a triangle has sides 6 feet and 9 feet and the perimeter is 23 feet, how long is the third side?
8 feet
If a triangle has sides 14 centimeters and 18 centimeters and the perimeter is 49 centimeters, how long is the third side?
A triangular flag has base one foot and height 1.5 foot. What is its area?
0.75 sq. ft.
A triangular window has base eight feet and height six feet. What is its area?
What is the base of a triangle with area 207 square inches and height 18 inches?
23 inches
What is the height of a triangle with area 893 square inches and base 38 inches?
One angle of a right triangle measures 33 degrees. What is the measure of the other small angle?
57
One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?
One angle of a right triangle measures 22.5 degrees. What is the measure of the other small angle?
67.5
One angle of a right triangle measures 36.5 degrees. What is the measure of the other small angle?
The perimeter of a triangle is 39 feet. One side of the triangle is one foot longer than the second side. The third side is two feet longer than the second side. Find the length of each side.
13 ft., 12 ft., 14 ft.
The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.
One side of a triangle is twice the shortest side. The third side is five feet more than the shortest side. The perimeter is 17 feet. Find the lengths of all three sides.
3 ft., 6 ft., 8 ft.
One side of a triangle is three times the shortest side. The third side is three feet more than the shortest side. The perimeter is 13 feet. Find the lengths of all three sides.
The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.
The measure of the smallest angle of a right triangle is 20° less than the measure of the next larger angle. Find the measures of all three angles.
The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.
The angles in a triangle are such that one angle is 20° more than the smallest angle, while the third angle is three times as large as the smallest angle. Find the measures of all three angles.
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