Question

Please answer KM, sin L, cos L, tan L, sin M, cos M, tan L.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Find the value of KM

Using Pythagoras' Theorem,

`\begin{gathered} hypotenuse^2=opposite^2+adjacent^2 \\ hypotenuse=34,adjacent=16,opposite=? \end{gathered}`

By substitution,

`\begin{gathered} 34^2=opposite^2+16^2 \\ opposite^2=34^2-16^2 \\ opposite^2=900 \\ opposite=√(900)=30 \end{gathered}`

KM = 30

STEP 2: Find the required ratio

To get sin L:

`\begin{gathered} \sin\theta=(opp)/(hyp) \\ By\text{ substitution,} \\ \sin L=(30)/(34)=(15)/(17) \end{gathered}`

sin L = 15/17

To get cos L

`\begin{gathered} \cos\theta=(adjacent)/(hypotenuse) \\ \cos L=(16)/(34)=(8)/(17) \end{gathered}`

cos L = 8/17

To get tan L

`\begin{gathered} \tan\theta=(opposite)/(adjacent) \\ By\text{ substitution,} \\ \tan L=(30)/(16)=(15)/(8) \end{gathered}`

tan L = 15/8

STEP 3: Find the ratios for angle M

To get sin M

`\begin{gathered} \sin\theta=(opp)/(hyp) \\ By\text{ substitution,} \\ \sin M=(16)/(34)=(8)/(17) \end{gathered}`

sin M = 8/17

To get cos M

`\begin{gathered} \cos\theta=(adj)/(hyp) \\ By\text{ substitution,} \\ \cos M=(30)/(34)=(15)/(17) \end{gathered}`

cos M = 15/17

tan L has been done in Step 2

tan L = 15/8