[G.SRT.8] Similarity, Right Triangles, and Trigonometry #8

Objective

Common Core Text:

• • [G.SRT.8] (*) Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

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Explanation

The applications of trigonometric ratios are endless. I used these in most of my classes during college, even though the classes were very different.

In fact, just today I benefited tremendously by knowing how to use these. If I hadn't, I might have lost about $100 in rental fees, and made some family members mad by wasting their time. Let's look some examples.

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Example

Some details of this story have been changed for simplicity.

Mr. Rose had a tremendous opportunity. Someone in Kingsburg was giving away an upright piano (worth maybe $4000) for free! All Mr. Rose had to do was come and get it.

The problem is, Mr. Rose has a very steep driveway. He needed to calculate if he could even get the piano up the driveway into his garage.

First, Mr. Rose needed to calculate the angle of his driveway. This would tell him how much force he would need to push the piano up the driveway

After thinking, Mr. Rose decided decided trigonometric ratios would be the easiest approach. He needed to make a triangle, so he measured the length of the driveway, and the height of the garage from the road. The driveway was 25 feet long, and the height was 15 feet.

Now that Mr. Rose had his measurements, he wanted to draw the triangle differently so he could calculate the angle he really wanted.

Mr. Rose saw that for the angle he wanted, he had measured the opposite side and the hypotenuse. That meant sine would be the best trigonometric ratio to use.

Sine of an Angle =