Question

Can someone explain how to use sin cos and tan on right angled triangles

Answer 1

Here is the formula of sin cos tan :

sin x = opposite/hypotenuse

cos x = adjacent / hypotenuse

tan x = opposite / adjacent

d = hypotenuse

x = the angle known in your pic

like example if in your picture:

adjacent = 26.5

if want to find the d

cos x = adjacent / hypotenuse

cos 56 = 26.5 / d

d = 26.5 : cos(56)

d = 47.390 (3 significant figures)

and if want to find the opposite

tan x = opposite/adjacent

tan 56 = opposite/ 26.5

opposite = 26.5 × tan(56)

opposite = 39.288

-> Sorry if im wrong

Answer 2

Answer: d = 47.3897287242421 approximately

Round this however you need to

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Step-by-step explanation:

The reference angle is 56 degrees. The side 26.5 is adjacent to this angle as it is the leg closest to the angle (in contrast to the opposite leg or opposite side that is furthest from the reference angle)

The hypotenuse is d. The hypotenuse is always the longest side. The longest side is always opposite the largest angle of a triangle.

We will use the cosine ratio as it is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

cos(56) = 26.5/d

d*cos(56) = 26.5

d = 26.5/cos(56)

d = 47.3897287242421

You use your calculator for the last step shown above. Make sure your calculator is in degree mode. Round that value however you need to.