Question

HELP THIS IS TRIGONOMETRY OR GEOMETRY!!!

Answer 1

Answer: PR=14.5.

Explanation:

1. If the area of PQR is 50, then (QR*PQ)/2=50, so QR*PQ=100 (the area of a triangle is the base*height/2).

2, The tangent of an angle is (the opposite side)/(the adjacent side). So, the tangent of angle P=QR/PQ. Angle P is 36 degrees, and the tangent of 36 degrees is 0.726542528. We can substitute this into the equation we found to get 0.726542528=QR/PQ.

3. Using the equations we found in Steps 1 and 2, we can create a system of equations:

`\left \{ {{QR*PQ=100} \atop {QR/PQ=0.726542528}} \right.`

We can solve this system of equations to get PQ=11.7319 and QR=8.52375.

4. Using Pythagorean theorem, we can say that PR^2=QR^2+PQ^2. If we substitute the values of PQ and QR into the equation, we can come to the conclusion that PR=14.5014410206, which simplifies to PR=14.5.

Answer 2

Answer:PR = 14.48 units

Explanation:

The diagram of the right angle triangle PQR is shown in the attached photo.

Let x represent PQ

Let y represent PR

Let z represent QR

Applying trigonometric ratio

Tan # = opposite side/adjacent side

Tan 36 = z/x

z = xtan36 = 0.7265x

Area of the triangle is 50

The formula for determining the area of a triangle is expressed as

Area = 1/2 base × height

50 = 1/2 × z × x

zx = 50 × 2 = 100 - - - - - - - - -1

Substituting z = 0.7265x into equation 1, it becomes

0.7265x × x = 100

0.7265x^2 = 100

x^2 = 100/0.7265 = 137.65

x = √137.65 = 11.73

z = 0.7265x = 0.7265 × 11.73 = 8.52

To determine y, we will apply Pythagoras theorem which is expressed as

Hypotenuse^2 = opposite side^2 + adjacent side^2

Looking at triangle PQR,

Hypotenuse = y

Opposite = 8.52

Adjacent = 11.73

Therefore,

y^2 = 11.73^2 + 8.52^2

y^2 = 210.1833

y = √210.1833 = 14.48