Astatue is mounted on top of a 42 foot hill. from the base of the hill to where you are standing is 73 feet and the statue subtends an angle of 10.3° to where you are standing. find the height of the statue.

  19.72 ft

Step-by-step explanation:

You know the tangent of an angle is the ratio of the opposite side to the adjacent side of the right triangle. So, the angle α to the bottom of the statue is ...

  tan(α) = (42 ft)/(73 ft)

  α = arctan(42/73) ≈ 29.914°

Then the angle to the top of the statue is ...

  β = 10.3° +29.914° = 40.214°

The same tangent relationship tells us the height to the top of the statue from the base of the hill is ...

  tan(β) = (height to top)/(73 ft)

Multiplying by 73 ft gives ...

  height to top of statue = (73 ft)·tan(40.214°) = 61.72 ft

So, the height of the statue is the difference between the heights of its top and its base:

  statue height = 61.72 ft - 42 ft

  statue height = 19.72 ft

answer is:

1.75 pounds

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1