Application of Trigonometry in Daily life

I have a question here on trigonometry. Can you help me in solving it?

A boy standing at the edge of a canal sees the top of a tree at an elevation of 70^o . Stepping 10 metres back, he sees it at an elevation of 25^o. The boy is 1.5 metres tall. How wide is the canal and how tall is the tree?

Let us solve this question using a simple quiz

Q1: What are the only types of triangles we can use trigonometry with?

• Obtuse

• Right

• Acute

• Any triangle

The figure shows the line diagram of the question;

TR is the tree, BY is the first position of the boy, NP is his new position. Correct!?

Q2: What are the lengths NP and PY respectively?

• 1.5meters and 15meters

• 2meters and 10meters

• 1.5meters and 10meters

• 2meters and 15meters

Answer explanation

The length NP represents height of the boy which is equal to 1.5m

PY is the length which the boy stepped back which is equal to 10m

Answer explanation

Additional information:

Angles TNL and TBL are known as angle of elevation

Angle TBL is the angle of elevation when boy looked at the tree before stepping back which is 70 degrees

Angle TNL is the angle of elevation when boy looked at the tree after stepping back which is 25 degrees

Now we are done with the lengths and angles in the question

Here, TR(height of tree)= TL+ 1.5meters and YR(width of canal)=BL , Correct?

Q: Which is the trig function relates the opposite side and the adjacent side?

• sine

• cosine

• tan

• All of the above

Answer explanation

Additional information:

1. trig function relates the opposite side and hypotenuse is sine function

2.trig function relates the hypotenuse and the adjacent side is cosine function

• y/x

• x/y

• x/(y+10)

• (x+10)/y

• (y+10)/x

• y/(x+10)

Now we got the equation,

y = (x + 10) tan 25^o = 0.4663x + 4.663..............equation1

y = x tan 70^o = 2.7475x..................equation2

from the last 2 questions

Right?

Q: What is the approximate value of x by solving equations 1 and 2?

(Make use of calculator)

• 2meters

• 4 meters

• 2.5meters

• 3 meters

Since we got x, we can easily get y, isn't it?

What is the approximate value of y?

• 6meters

• 5meters

• 5.6 meters

• 4.6meters

Since x is the width of the canal, we got width of canal = 2 meters

Q: Now, What is the height of the tree?

• 3.5 meters

• 7.1 meters

• 7 meters

• 3 meters

Answer explanation

Height of the tree= TR

=TL+LR

= y+ 1.5 meters

= 5.6 + 1.5

= 7.1 meters

Thanks to all learners for helping me in solving the question

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