The pilot of a hot-air balloon measures the angle of depression to a landing spot to be 20.5o.

Question

The pilot of a hot-air balloon measures the angle of depression to a landing spot to be 20.5o. If the pilot's altitude is 90m, what is the horizontal distance between the balloon and the landing spot?

I need to know the measure of angle theta that I will use to help me set up my trig ratio.

Will I use (sin/cos/tan) to set up the problem?

What equation will I used to solve this problem?

What is the horizontal distance between the balloon and the landing spot?

Answer 1

Draw and label a diagram.

B is at the balloon.

C is at the right angle directly below the balloon.

A is at the landing spot.

 

m∠A = 20.5°         alternate interior angles

 

tan 20.5° = 90 / CA

0.372884679 ≈ 90 / CA  use calculator

0.372884679 CA ≈ 90     multiply both sides by CA

CA ≈ 240.7                    divide both sides by that big decimal

 

The horizontal distance is approximately two hundred forty-one meters.

Answer 2

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Answer 3

Hi Sami,

 

The angle of depression is the angle from where the hot-air balloon is downwards towards the ground. 

 

It will definitely help for you to draw this problem out. Start with the ground. Then draw a straight vertical line up(can be whatever size you prefer) and draw your hot-air balloon. Now from your hot air balloon, draw a straight horizontal line to the right. From this line downwards(clock-wise) you have a 20.5 degree angle. Draw a diagonal line about 20.5 degrees below the horizontal line so that it reaches the "ground." You should now see that the 20.5 degree angle is not inside our triangle yet.

 

So 90-20.5=69.5. We have a right angle between the ground and the vertical line to the balloon. That means the third angle in our triangle is 20.5 (which makes sense because in a right triangle, the 2 non-right angles must equal 90 degrees). 

 

This drawing should make how to calculate the horizontal distance between the balloon and landing spot pretty obvious. 

 

Your teacher may have also taught you the following to remember whether to use Sin, Cos, or Tan:

 

SOH... Sine: sin(θ) = Opposite / Hypotenuse
CAH...Cosine: cos(θ) = Adjacent / Hypotenuse
TOA...Tangent: tan(θ) = Opposite / Adjacent

 

So at this point we know the angle and we know the Opposite side value-90m. We need to find the value of the adjacent side, so pick the equation that includes the opposite and adjacent. And the angle we need is from the ground to the adjacent, which is 20.5. 

 

Let me know if you have any additional questions.

 

Brittany