SOLUTION: In the diagram below, we know \tan \theta = \frac{3}{4}. Find the area of the triangle.
The triangle is right, and the hypotenuse is 80.
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Triangles
-> SOLUTION: In the diagram below, we know \tan \theta = \frac{3}{4}. Find the area of the triangle.
The triangle is right, and the hypotenuse is 80.
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Explanation
tangent is the ratio of opposite over adjacent
tan(theta) = 3/4
tan(theta) = opposite/adjacent
opposite/adjacent = 3/4
If we didn't know anything about the hypotenuse, then we could have a 3-4-5 right triangle. Or we might have a 6-8-10 right triangle.
In general we have a 3x-4x-5x right triangle for some positive real number x.
The hypotenuse is given to be 80 units long, so,
5x = 80
x = 80/5
x = 16
The two legs are 3x = 3*16 = 48 and 4x = 4*16 = 64
area = 0.5*base*height = 0.5*48*64 = 1536 square units
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