The angles of elevation of a balloon from two points A and C on level ground are 24.5 and 41.3, respectively . Points A and C are 3.5 miles apart and the balloon is between the points. Approximate the height of the balloon above the ground.

height of the balloon = 1.0494 miles        

Step-by-step explanation:

I drew a triangle and labeled angles A, B and C and sides a, b and c.

a = (c · sin A) / sin C = (3.5 · sin 24.5°) / sin 114.2° = 1.4514 / 0.9121 = 1.59 miles

now we have a 90° triangle

h = (a · sin B) / sin 90° = (1.59 · sin 41.3°) / sin 90° = 1.0494 / 1 = 1.0494 miles

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!