A flagpole at a right angle to the horizontal is located on a slope that makes an angle of \large 10^\circ with the horizontal. The flagpole casts a 30-meter shadow down the slope. The angle of elevation from the tip of the shadow to the sun is \large 25^\circ. What is the length of the flagpole to the nearest tenth of a meter?

13.1 m

Step-by-step explanation:

From the diagram attached :

Using Sine rule :

a / sin A = b/Sin B = c / sin C

h / sin 25 = 30 / sin 75

Cross multiply :

h * sin 75 = 30 * sin 25

0.9659258 * h = 30 * 0.4226182

h = 12.678547 / 0.9659258

h = 13.125798

Length of flagpole h = 13.1 m

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15