Question

2. What is the length of the hypotenuse k?

Answer 1

k ≈ 50.77

Explanation:

using the cosine ratio in the right triangle

cos19° =
`(adjacent)/(hypotenuse)` =
`(48)/(k)` ( multiply both sides by k )

k × cos19° = 48 ( divide both sides by cos19° )

k =
`(48)/(cos19)` ≈ 50.77 ( to 2 dec. places )

Answer 2

Hi :)

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We'll use sohcahtoa to solve this problem

`\Large\boxed{\begin{tabular}1 \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~/ \text{hyp}\\\sf{Cah} & Adj / \text{hyp}\\\sf{Toa} & Opp / \text{adj} \end{tabular}}`

Looking at our triangle, we can clearly see that we have :

• adj. side = 48 (adjacent to the angle)
• hyp. k (the one we need)

Set up the ratio

`\longrightarrow\darkblue\sf{cos(19)=(48)/(k)}`

solve for k

`\longrightarrow\darkblue\sf{k\cos(19)=48}` > multiply both sides by k to clear the fraction

`\longrightarrow\darkblue\sf{k=(48)/(\cos(19))}` > divide both sides by cos (19)

`\star\longrightarrow\darkblue\sf{k\approx50.77}\star`

`\tt{Learn~More ; Work\ Harder}`

:)