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How do I find the base of this triangle? 36degrees50 degrees94 degrees Height is 85

How do I find the base of this triangle? 36degrees50 degrees94 degrees Height is 85-example-1

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Find the base of the given triangle

We need to add two variables to find the base. They can be seen in the image below:

The length of the base is then calculated as B = x + y

Let's focus on the triangle at the left. We are given its height h=85 and the base angle of 36°.

Recalling the tangent of an angle relates the opposite side of the triangle to its adjacent side as follows:


\tan 36^o=(85)/(x)

Solving for x:


x=(85)/(\tan 36^o)

Calculating:


x=(85)/(0.7265)=116.99

Now we use the other triangle at the right:


\tan 50^o=(85)/(y)

Solving for y:


y=(85)/(\tan 50^o)

Calculating:


y=(85)/(1.1918)=71.32

Finally, the length of the base is:

B = x + y = 116.99 + 71.32 = 188.32

The length of the base is 188.32 units

How do I find the base of this triangle? 36degrees50 degrees94 degrees Height is 85-example-1
User Darielle
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