Question

kuta software - infinite geometry
name
solving right triangles
date
find the missing side. round to the nearest tenth.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Identify trig ratio for 1)

We have adjacent side $6$, angle $72^\circ$, need opposite side $x$. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(72^\circ)=\frac{x}{6}$

Step2: Solve for x in 1)

$x=6\times\tan(72^\circ)$
$x\approx6\times3.0777=18.5$

Step3: Identify trig ratio for 2)

We have hypotenuse $6$, angle $73^\circ$, need adjacent side $x$. Use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(73^\circ)=\frac{x}{6}$

Step4: Solve for x in 2)

$x=6\times\cos(73^\circ)$
$x\approx6\times0.2924=1.8$

Step5: Identify trig ratio for 3)

We have adjacent side $12$, angle $24^\circ$, need opposite side $x$. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(24^\circ)=\frac{x}{12}$

Step6: Solve for x in 3)

$x=12\times\tan(24^\circ)$
$x\approx12\times0.4452=5.3$

Step7: Identify trig ratio for 4)

We have adjacent side $12$, angle $37^\circ$, need opposite side $x$. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(37^\circ)=\frac{x}{12}$

Step8: Solve for x in 4)

$x=12\times\tan(37^\circ)$
$x\approx12\times0.7536=9.0$

Step9: Identify trig ratio for 5)

We have opposite side $14$, angle $49^\circ$, need adjacent side $x$. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(49^\circ)=\frac{14}{x}$

Step10: Solve for x in 5)

$x=\frac{14}{\tan(49^\circ)}$
$x\approx\frac{14}{1.1504}=12.2$

Step11: Identify trig ratio for 6)

We have opposite side $14$, angle $51^\circ$, need hypotenuse $x$. Use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(51^\circ)=\frac{14}{x}$

Step12: Solve for x in 6)

$x=\frac{14}{\sin(51^\circ)}$
$x\approx\frac{14}{0.7771}=18.0$

Step13: Identify trig ratio for 7)

We have adjacent side $16$, angle $63^\circ$, need hypotenuse $x$. Use cosine: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(63^\circ)=\frac{16}{x}$

Step14: Solve for x in 7)

$x=\frac{16}{\cos(63^\circ)}$
$x\approx\frac{16}{0.4540}=35.2$

Step15: Identify trig ratio for 8)

We have opposite side $16$, angle $15^\circ$, need hypotenuse $x$. Use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(15^\circ)=\frac{16}{x}$

Step16: Solve for x in 8)

$x=\frac{16}{\sin(15^\circ)}$
$x\approx\frac{16}{0.2588}=61.8$

Answer:

1. $18.5$
2. $1.8$
3. $5.3$
4. $9.0$
5. $12.2$
6. $18.0$
7. $35.2$
8. $61.8$