What is the value of x? round to the nearest hundredth

question 1 options:

a. 34.61
b.74.23
c.175.64
d.193.79

Using the law of Cosine:

Cos(angle) = Adjacent Leg / Hypotenuse

Cos(65) = x / 81.9

x = 81.9 x cos(65)

x = 34.61

The answer is A.

Option A. 34.61

Step-by-step explanation:

The given triangle is a right angle triangle with the measure of one angle = 65°, adjacent side or base of the triangle = x and largest side (hypotenuse) of the triangle = 81.90

Now we have to calculate the measure of x.

Now in the right angle triangle we apply cosine rule.

cos65° =

cos65° =

0.4223 =

x = (0.4223)×(81.90)

x = 34.61

Option A. 34.61 is the correct option.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

i think the correct option is the second option.