Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side

Practice Questions

Common Core: High School - Geometry › Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side

Questions
10
1

Is the following statement True or False?

In order to use this formula, you only need to know two of the triangles sides' lengths.

2

Using the triangle below, find the area then solve for .

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3

Is the following statement True or False?

We want to use the formula . Consider an obtuse triangle . We know the lengths of and , but only know the angle for . We are still able to use this formula.

4

Stephanie is building a triangular garden in her backyard. She has cut wood for the sides with lengths of 5, 4, and 3 feet. Knowing that the height from the vertex $A$ to the base formed by the line $CB$ is 1.778 feet, first find the area that will be in the garden and then calculate each angle that Stephanie will have to put the boards together in order for the lengths to fit just right. Round your answer to the third decimal place if needed.

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5

Complete the statement by choosing from one of the following

Regarding the triangle below, to find the area using the formula , I assume that ______

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6

Solve for x using the formula given that the area of the following triangle is (round to the second decimal place if needed).

7

You are making your friend a triangular fabric decoration for their home. It has ripped so you need to go buy new fabric. The fabric you are buying is $3 per square foot. Using the dimensions below, how much money do you need to buy enough fabric?

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8

Given the triangle below, find the area and round to the second decimal place (in degrees).

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9

Using the information from the following triangle, find the area. Round to the second decimal place.

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10

Given the triangle below, what is the formula for finding the area?

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