trig-word-problems-height-of-a-light-pole

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Word problems solved using trigonometry.

Trig can be used to find length,width,angles, and many more measurements of shapes and objects. The video solves the following word problem.

A 5 foot person standing 10 feet from a street light casts a 14 foot shadow. What is the height of the streetlight?

Transcript

A five and a half foot person stands 10 feet from a another person (this our light pole here) and the shadow created by the person is 10 feet and the person is 5.5 feet tall. What is the angle here, and how tall is the streetlight? We actually are trying to figure this out and you could do several things to figure this out. You could use proportions or trig and since this is a trig unit we will use trig. Let's first figure what this angle is,once we figure the angle, do you see how we have two triangles we will use to find x and we can use the larger triangle to here that we can use once we find x to find the height of the pole. Let's figure out x. Using just the small triangle, which two sides do we have? We have opposite over adjacent. The tangent of x equals 5.5 over 14. Which is the opposite over adjacent. Since we are solving for an angle we know we need to do? We have to use our inverse button. We will use the second tangent of 5.5 divided by 14 and we get the angle measure of 21.447 We will round to 21 degrees. Now we can use that to solve for the height of the light. Now we use opposite, we don't know this side so it must be this side we are going to use. Notice how long is this whole side? This is 10 plus 14 and together it is 24. So we will take the tangent of 21 is equal to the opposite x over the adjacent which is 24. The tangent of 24 is equal to the opposite over adjacent. This is a simple problem cause we don't even have to divide. So the tangent of 21 times 24 is 9.2. Cross product, and x equal to 9.2 and this unit measure was in feet, and that is how you do it. The light post is 9.2 feet tall.

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Tagged under: trig,trigonometry,trig word problems,geometry,tangent, adjacent,math,maths,moomoomath

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