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Mathematics : Some Applications of Trigonometry

Short Answer Type

121. An observer 1.70 m tall, is 12.90 m away from a tower 14.60 m high. Determine the angle of elevation of the top of the tower from his eye.

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122. A tower in a city is 150 m high and a multi-storyed hotel at the city centre is 20 m high. The angle of elevation of the top of the tower of the top of the hotel is 5°. A building h mts high is situated on the straight road connceting the tower with the city centre at a distance of 1.2 km from the tower. Find the value of h, if the top of the hotel, the top of the building and the top of the tower are in a straight line. Also, find the distance of the tower from the city centre.

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123.

A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches at a height of 90 m on the wall and makes an angle of 60° with the ground. If while resting at the same point on the path, it were made to lean against the other wall, it would have made an angle of 45° with the ground. Find the height it would have reached on the second wall.

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124. Two boats approach a lighthouse in mid-sea from opposite directions. The angles of elevation of the top of the lighthouse from two boats are 30 and 45° respectively. If the distance between two boats is 100 m, find the height of the lighthouse.

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125. The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sunrays meet the ground at an angle of 60°. Find the angle between the sunrays and the ground at the time of longer shadow.

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126. The line joining the top of a hill to the foot of the hill makes angle of 30° with the horizontal through the foot of the hill. There is one temple at the top of the hill and a guest house half way from the foot to the top. The tops of the temple and of the guest house both make an elevation of 45° at the foot of the hill. If the guest house is 100 m away from the foot of the hill. Find the height of the guest house and the temple.

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127. From the top of a building 100 m. high, the angle of elevation of the top of a tower is found to be 60° and the angle of the top of a tower is found to be 60° and the angle of depression of the base of the tower is 45°. Find the height of the tower and its distance on the ground from the building.

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128. Two ships are sailing in the sea on either side of the light-house, the angles of depression of two ships as observed from the top of light-house are 60° and 45° respectively. If the distance

between the ships is 200

open parentheses fraction numerator square root of 3 plus 1 over denominator square root of 3 end fraction close parentheses

find the height of the light-house

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129. An aeroplane when 300 metres high passes vertically above another aeroplane at an instance when their angles of elevation at the same observation point are 60° and 45° respectively. How many metres higher is the one than the other?

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130. The angle of elevation of the top of a tower from a point A on the ground is 30°, On moving a distance of 20 metres towards the foot of the tower a point 13 the angle of elevation increases to 60°. Find the height of the tower and distance of the tower from the point A..

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