Photo AI

A tree 32 m high casts a shadow 63 m long - Junior Cycle Mathematics - Question Question 1 - 2013

Question Question 1

A tree 32 m high casts a shadow 63 m long. Calculate θ, the angle of elevation of the sun. Give your answer in degrees and minutes (correct to the nearest minute).

Worked Solution & Example Answer:A tree 32 m high casts a shadow 63 m long - Junior Cycle Mathematics - Question Question 1 - 2013

Step 1

Calculate tan(θ)

96%

114 rated

Answer

To find the angle of elevation of the sun, we can use the tangent function. Here, we have:

$\tan(θ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{32}{63}$

Step 2

Calculate θ using the arctan function

99%

104 rated

Answer

Now, we can calculate θ by taking the arctan of the ratio:

$θ = \tan^{-1}\left(\frac{32}{63}\right)$

Using a calculator, we find:

$θ \approx 26.9277°$

Step 3

Convert decimal to degrees and minutes

96%

101 rated

Answer

To express the decimal part in minutes, take the decimal (0.9277) and multiply by 60:

$0.9277 \times 60 \approx 55.662$

This gives approximately 55 minutes. Therefore, we can round the total and express the angle as:

$θ \approx 26° 55'$

Join the Junior Cycle students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;