Example problem solving trigonometry using SOH CAH TOA with a ladder and a kite.

Let’s solve Example 2 step by step.

We are told:
- A kite is 60 meters above the ground → this is the opposite side (relative to the angle of elevation).
- The string makes an angle of elevation of 42° with the ground → that’s our angle θ.
- We need to find how long the wire is → that’s the hypotenuse (the string itself).

So we have:
- Opposite = 60 m
- Angle = 42°
- Hypotenuse = ? (let’s call it H)

Which trig ratio uses opposite and hypotenuse?
→ Sine: sin(θ) = opposite / hypotenuse

So:

sin(42°) = 60 / H

Now solve for H:

H = 60 / sin(42°)

Let’s calculate sin(42°). Using a calculator:

sin(42°) ≈ 0.6691

Then:

H ≈ 60 / 0.6691 ≈ 89.67 meters

Let me double-check that division:

60 ÷ 0.6691 = ?

Do it carefully:

0.6691 × 89 = 0.6691 × 90 - 0.6691 = 60.219 - 0.6691 = 59.5499 → too low

Try 89.7:

0.6691 × 89.7 = let’s compute:

First, 0.6691 × 90 = 60.219
Minus 0.6691 × 0.3 = 0.20073
So 60.219 - 0.20073 = 60.01827 → very close to 60!

So H ≈ 89.7 meters is accurate enough.

Actually, using more precise calculation:

sin(42°) = sin(42) ≈ 0.669130606...

60 0.669130606 ≈ 89.672...

Rounded to one decimal place: 89.7 meters

But since the problem gives numbers like “60m” and “42°”, which are whole numbers, maybe they expect rounding to nearest meter? Let’s check:

89.672… → rounds to 90 meters if rounding to nearest whole number.

Wait — let’s see what the context expects. In Example 1, they gave answer as 42°, even though calculator showed 41.8° — so they rounded to nearest degree.

Here, length — probably reasonable to give to nearest meter or one decimal.

But let’s be precise: 60 / sin(42°) = exactly?

Using calculator: 60 ÷ sin(42) = 60 ÷ 0.6691306063588582 = 89.672277...

So approximately 89.7 meters

I think 89.7 m is fine. But let’s confirm units — yes, meters.

Final Answer:
89.7