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The measures of two angles of a triangle are 55 and 82 degrees. Find the measure of the third angle.
| Step 1. Read the problem. Draw the figure and label it with the given information. |
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| Step 2. Identify what you are looking for. | the measure of the third angle in a triangle |
| Step 3. Name. Choose a variable to represent it. | Let the measure of the angle. |
| Step 4. Translate. | |
| Write the appropriate formula and substitute. | |
| Step 5. Solve the equation. | |
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Step 6. Check.
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| Step 7. Answer the question. | The measure of the third angle is 43 degrees. |
The measures of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.
21 degrees
The measures of two angles of a triangle are 49 and 75 degrees. Find the measure of the third angle.
56 degrees
The perimeter of a triangular garden is 24 feet. The lengths of two sides are four feet and nine feet. How long is the third side?
| Step 1. Read the problem. Draw the figure and label it with the given information. |
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| Step 2. Identify what you are looking for. | length of the third side of a triangle |
| Step 3. Name. Choose a variable to represent it. | Let the third side. |
| Step 4. Translate. | |
| Write the appropriate formula and substitute. |
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| Substitute in the given information. |
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| Step 5. Solve the equation. |
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Step 6. Check.
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| Step 7. Answer the question. | The third side is 11 feet long. |
The perimeter of a triangular garden is 48 feet. The lengths of two sides are 18 feet and 22 feet. How long is the third side?
8 feet
The lengths of two sides of a triangular window are seven feet and five feet. The perimeter is 18 feet. How long is the third side?
6 feet
The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window’s height?
| Step 1. Read the problem. Draw the figure and label it with the given information. |
Area |
| Step 2. Identify what you are looking for. | height of a triangle |
| Step 3. Name. Choose a variable to represent it. | Let the height. |
| Step 4. Translate. | |
| Write the appropriate formula. |
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| Substitute in the given information. |
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| Step 5. Solve the equation. |
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Step 6. Check.
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| Step 7. Answer the question. | The height of the triangle is 12 meters. |
The area of a triangular painting is 126 square inches. The base is 18 inches. What is the height?
14 inches
A triangular tent door has area 15 square feet. The height is five feet. What is the base?
6 feet
The triangle properties we used so far apply to all triangles. Now we will look at one specific type of triangle—a right triangle. A right triangle has one angle, which we usually mark with a small square in the corner.
A right triangle has one angle, which is often marked with a square at the vertex.
One angle of a right triangle measures What is the measure of the third angle?
| Step 1. Read the problem. Draw the figure and label it with the given information. |
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| Step 2. Identify what you are looking for. | the measure of an angle |
| Step 3. Name. Choose a variable to represent it. | Let the measure of an angle. |
| Step 4. Translate. | |
| Write the appropriate formula and substitute. | |
| Step 5. Solve the equation. | |
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Step 6. Check.
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| Step 7. Answer the question. | The measure of the third angle is 62 ° . |
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