Question

Ahmad is driving on a road. He observed that the road is inclined at an angle of 6 degree .He travelled 1.5km on this inclined road. How high above road level is Ahmad??

Answer 1

Given:

Ahmad is traveling on a road at an inclination of $6^\circ$.

Distance traveled = 1.5 km

To find:

Height of Ahmad above road level = ?

Solution:

The given situation can be represented in the form of a right angled triangle $\triangle ABC$ as shown in the attached figure in answer area.

The side BC represents the road level.

The distance traveled by Ahmad is AC = 1.5 km

$\angle C =6^\circ$

And the side AB is to be found.

We can use trigonometric identity of Sine here to find AB.

We know that:

$sin\theta =\dfrac{Perpendicular}{Hypotenuse}$

$sinC=\dfrac{AB}{AC}\\\Rightarrow sin6=\dfrac{AB}{1.5}\\\Rightarrow AB = 1.5 \times sin6\\\Rightarrow AB = 1.5 \times 0.1045\\\Rightarrow AB = 0.1568\ km \ or\ 156.8 \ m$

So, Ahmad is 0.1568 km or 156.8 m high above road level.

Answer 2

$Given \: inclination \: of \: road \:\theta = 6\degree$

$Distance \: travelled \: on \: inclined \:road$

$AC = 1.5 \:km$

$= 1.5 \times 1000 \:m$

$= 1500 \: m$

$Height \:of \: the \: road = BC\: m$

$Now, In \: \triangle ABC ,$

$sin \theta = \frac{BC}{AC}$

$\implies sin 6 \degree = \frac{BC}{1500}$

$\implies 0.1045 = \frac{BC}{1500}$

$\implies BC = 0.1045 \times 1500$

$\implies BC = 156.75 \:m$

Therefore.,

$\red{Height \:of \: the \: road} \green { = 156.75 \:m }$

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