Question

right triangle quiz a 2019
name
date
period

1. use the pythagorean theorem to find the missing side length. show your work!

1. you start driving west for 5 miles, turn left, and drive south for another 8 miles. at the end of driving, what is your distance from your starting point?

a. 41 mi
b. √89 mi
c. 13 mi
d. 34.1 mi

1. which segment is adjacent to ∠j?

a. ( overline{ij} )
b. ( overline{jk} )
c. ( overline{ih} )
d. ( overline{jh} )

1. which segment is the hypotenuse?

a. ( overline{ij} )
b. ( overline{jk} )
c. ( overline{ih} )
d. ( overline{jh} )

1. which segment is opposite to ∠j?

a. ( overline{mk} )
b. ( overline{ml} )
c. ( overline{kl} )
d. ( overline{jm} )

7 - 9. find the indicated trigonometric ratio as a simplified fraction.

1. ( sin l = )

1. ( cos l = )

1. ( \tan l = )

for the triangle with sides ( mk = 30 ), ( kl = 16 ), ( ml = 34 ):

a. ( \frac{8}{17} )
b. ( \frac{15}{17} )
c. ( \frac{8}{15} )
d. ( \frac{15}{8} )

Explanation:

7. $\sin L$

Step 1: Recall Sine Definition

Sine of an angle in a right triangle is $\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle L$, opposite side is $MK = 30$, hypotenuse is $ML = 34$.

Step 2: Calculate $\sin L$

$\sin L = \frac{MK}{ML} = \frac{30}{34} = \frac{15}{17}$.

8. $\cos L$

Step 1: Recall Cosine Definition

Cosine of an angle in a right triangle is $\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle L$, adjacent side is $KL = 16$, hypotenuse is $ML = 34$.

Step 2: Calculate $\cos L$

$\cos L = \frac{KL}{ML} = \frac{16}{34} = \frac{8}{17}$.

9. $\tan L$

Step 1: Recall Tangent Definition

Tangent of an angle in a right triangle is $\frac{\text{opposite}}{\text{adjacent}}$. For $\angle L$, opposite side is $MK = 30$, adjacent side is $KL = 16$.

Step 2: Calculate $\tan L$

$\tan L = \frac{MK}{KL} = \frac{30}{16} = \frac{15}{8}$.

Final Answers

1. $\boldsymbol{\frac{15}{17}}$ (Option b)
2. $\boldsymbol{\frac{8}{17}}$ (Option a)
3. $\boldsymbol{\frac{15}{8}}$ (Option d)

Answer:

7. $\sin L$

Step 1: Recall Sine Definition

Sine of an angle in a right triangle is $\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle L$, opposite side is $MK = 30$, hypotenuse is $ML = 34$.

Step 2: Calculate $\sin L$

$\sin L = \frac{MK}{ML} = \frac{30}{34} = \frac{15}{17}$.

8. $\cos L$

Step 1: Recall Cosine Definition

Cosine of an angle in a right triangle is $\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle L$, adjacent side is $KL = 16$, hypotenuse is $ML = 34$.

Step 2: Calculate $\cos L$

$\cos L = \frac{KL}{ML} = \frac{16}{34} = \frac{8}{17}$.

9. $\tan L$

Step 1: Recall Tangent Definition

Tangent of an angle in a right triangle is $\frac{\text{opposite}}{\text{adjacent}}$. For $\angle L$, opposite side is $MK = 30$, adjacent side is $KL = 16$.

Step 2: Calculate $\tan L$

$\tan L = \frac{MK}{KL} = \frac{30}{16} = \frac{15}{8}$.

Final Answers

1. $\boldsymbol{\frac{15}{17}}$ (Option b)
2. $\boldsymbol{\frac{8}{17}}$ (Option a)
3. $\boldsymbol{\frac{15}{8}}$ (Option d)