Hey, I just am stuck on this question. I was never good at word problems, or maybe I'm overthinking it. If you can help, that'd be great. Thanks so much!
It says: A chair is placed near a 26-ft tall tree. A right triangle is formed between the chair, the base of the tree, and the top of the tree. The angle formed at the top of the tree is 56°.
How far from the tree is the chair?
Answer in decimal form. Round only your final answer to the nearest tenth. (Once again, thank you!)
+2440 Since it is a right triangle, we need not use the law of sines or cosines but rather trigonometric ratios! In this case, we must use tangent!
Here's an acronym that may or may not help you remember which relationship is which:
| S | Sine |
| O | Opposite |
| H | Hypotenuse |
| C | Cosine |
| A | Adjacent |
| H | Hypotenuse |
| T | Tangent |
| O | Opposite |
| A | Adjacent |
How do you know where the reference is? Your point of refence is where the angle is located. I know to use tangent because I need to find the opposite angle of the angle of reference, 56, and I can use 26ft as given info. Let's solve for x:
| \(\frac{\tan56}{1}=\frac{x}{26}\) | Solve by cross-multiplying |
| \(26\tan56=x\) | This is the exact value. To find a decimal approximation, use a calculator that has the trigonometric ratios! |
| \(x=26\tan56\approx38.5ft\) | Of course, do not forget to label your answer with a unit |
One last note before you go!
Be sure that your calculator is in degree mode when evaluating \(26\tan56\). If it isn't, then your answer will be wildly different. In fact, in radian mode \(26\tan56\approx-15.8931\). This answer is definitely wrong as a side length can never be negative.
+2440 Since it is a right triangle, we need not use the law of sines or cosines but rather trigonometric ratios! In this case, we must use tangent!
Here's an acronym that may or may not help you remember which relationship is which:
| S | Sine |
| O | Opposite |
| H | Hypotenuse |
| C | Cosine |
| A | Adjacent |
| H | Hypotenuse |
| T | Tangent |
| O | Opposite |
| A | Adjacent |
How do you know where the reference is? Your point of refence is where the angle is located. I know to use tangent because I need to find the opposite angle of the angle of reference, 56, and I can use 26ft as given info. Let's solve for x:
| \(\frac{\tan56}{1}=\frac{x}{26}\) | Solve by cross-multiplying |
| \(26\tan56=x\) | This is the exact value. To find a decimal approximation, use a calculator that has the trigonometric ratios! |
| \(x=26\tan56\approx38.5ft\) | Of course, do not forget to label your answer with a unit |
One last note before you go!
Be sure that your calculator is in degree mode when evaluating \(26\tan56\). If it isn't, then your answer will be wildly different. In fact, in radian mode \(26\tan56\approx-15.8931\). This answer is definitely wrong as a side length can never be negative.
