Question

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critical thinking question:

1. write a new problem that is similar to the others on this worksheet. solve the question you wrote.

Explanation:

All problems use right triangle trigonometry: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$

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Problem 9

Step1: Identify sides/angle

$\theta=50^\circ$, hypotenuse=29, $x$=opposite

Step2: Use sine formula

$x=29\times\sin(50^\circ)$

Step3: Calculate value

$x\approx29\times0.7660\approx22.21$

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Problem 10

Step1: Identify sides/angle

$\theta=60^\circ$, opposite=21, $x$=adjacent

Step2: Use tangent formula

$x=\frac{21}{\tan(60^\circ)}$

Step3: Calculate value

$x=\frac{21}{\sqrt{3}}\approx12.12$

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Problem 11

Step1: Identify sides/angle

hypotenuse=28, adjacent=$x$, $\theta=18^\circ$

Step2: Use cosine formula

$x=28\times\cos(18^\circ)$

Step3: Calculate value

$x\approx28\times0.9511\approx26.63$

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Problem 12

Step1: Identify sides/angle

hypotenuse=22, $\theta=21^\circ$, $x$=adjacent

Step2: Use cosine formula

$x=22\times\cos(21^\circ)$

Step3: Calculate value

$x\approx22\times0.9336\approx20.54$

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Problem 13

Step1: Identify sides/angle

hypotenuse=28, $\theta=39^\circ$, $x$=adjacent

Step2: Use cosine formula

$x=28\times\cos(39^\circ)$

Step3: Calculate value

$x\approx28\times0.7771\approx21.76$

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Problem 14

Step1: Identify sides/angle

$\theta=45^\circ$, opposite=35, $x$=hypotenuse

Step2: Use sine formula

$x=\frac{35}{\sin(45^\circ)}$

Step3: Calculate value

$x=35\sqrt{2}\approx49.50$

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Problem 15

Step1: Identify sides/angle

adjacent=28, $\theta=47^\circ$, $x$=hypotenuse

Step2: Use cosine formula

$x=\frac{28}{\cos(47^\circ)}$

Step3: Calculate value

$x\approx\frac{28}{0.6820}\approx41.06$

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Problem 16

Step1: Identify sides/angle

hypotenuse=34, $\theta=59^\circ$, $x$=adjacent

Step2: Use cosine formula

$x=34\times\cos(59^\circ)$

Step3: Calculate value

$x\approx34\times0.5150\approx17.51$

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Problem 17

Step1: Create similar problem

Right triangle: right angle, $\theta=30^\circ$, hypotenuse=40, find opposite side $x$.

Step2: Solve the problem

Use sine: $x=40\times\sin(30^\circ)=40\times0.5=20$

Answer:

1. $\approx22.21$
2. $\approx12.12$
3. $\approx26.63$
4. $\approx20.54$
5. $\approx21.76$
6. $\approx49.50$
7. $\approx41.06$
8. $\approx17.51$
9. Created problem: Right triangle with a right angle, one acute angle of $30^\circ$, hypotenuse length 40. Find the length of the side opposite the $30^\circ$ angle.

Solution to created problem: $20$