Question

there is a small island in the middle of a 100m wide river and a tall tree stands on the island. p and q are the points directly opp to each other on two banks and in line with the tree. if the angle of elevation of the top of the tree from p and q are 3o and 45 respectively find the height of the tree​

Answer 1

Answer:

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Answer 2

$\huge\tt\red{Q}\tt\pink{U}\tt\blue{E}\tt\green{S}\tt\purple{T}\tt\orange{I}\tt\orange{O}\huge\tt\red{N}$

$\huge\tt\colorbox{pink}{Answer}$

$</p><p>Let \: \: OA \ \: : be \: \: the \ \: : tree \: \: of \: \: height \: \: h \: \: metre. \: \: In \ \: : triangle \ \: : POA \ \: : and \ \: : QOA, \: \: we \: \: have \: \: tan \ \: 30∘ \ \ = \frac{oa}{ op} \: \: and \: tan \: 45 ∘ = </p><p> \frac{oq}{oa} \\ </p><p></p><p> ⇒ 31 = \frac{op}{h} \\ </p><p> </p><p> and1= \frac{oq}{h}</p><p></p><p> </p><p> </p><p>⇒OP=3 \\ </p><p> \\ </p><p> hand \: OQ=h</p><p>⇒OP+OQ= 3</p><p> \\ </p><p> h+h</p><p>⇒PQ=( 3 +1)h \\ </p><p>⇒100=( 3 +1)h[∵PQ=100m]</p><p> +1 \\ </p><p>100m</p><p>⇒h= 2100( 3+1) m \\ </p><p>⇒h=50(1.732−1)m=36.6m \\ </p><p>Hence, the height of the tree is 36.6 m.</p><p>solution</p><p>$

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