Question

At Some Time Of The Day The Length Of The Shadow Of A Tower Is Equal To Its Height. What Is The Sun's Altitude At That Time.​

Answer 1

Answer:The value of θ is 45∘. Hence, the altitude of the sun is 45∘. Note: For a right angle triangle the trigonometric identity tanθ is the ratio of the opposite side to the adjacent side of the triangle.

Step-by-step explanation:The value of θ is 45∘. Hence, the altitude of the sun is 45∘. Note: For a right angle triangle the trigonometric identity tanθ is the ratio of the opposite side to the adjacent side of the triangle.

Answer 2

Answer :

45°.

Solution :

$\tt \bullet \: \: \: Let \: the \: length \: of \: shadow \: be \: x \: units.$

Now, given that.

• the length of the shadow of a tower is equal to its height.
• AB = BC = x units.
• Angle be θ.

$\rule{120}3$

⚝ Diagram.

$\setlength{\unitlength}{1 mm}}\begin{picture}(5,5)\put(-2.8,2){\line(-2,0){26.3}}\put(-3,2){\line(0,1){26}}\put(-29,-2){ \tt{C} }\put(-6,-2){ \tt{B} }\put(-2,26){ \tt{A} }\qbezier(-25.8,5)(-23,4)(-24,2)\put(-3,28){\line(-10,-1){26}}\put(-21,4){ \tt\theta }\end{picture}$

$\rule{120}3$

$\tt \implies tan \theta = \dfrac{Perpendicular}{Base}$

$\tt \implies tan \theta = \dfrac{\cancel{x}}{\cancel{x}}$

$\tt \implies tan \theta = 1.$

$\tt \implies tan \theta =tan45 \degree.$

$\tt \implies \theta =45 \degree.$