The angle of elevation of the top of a tower from two points 121 m and 144 m away from the foot of the tower on th same side are
1 answer:
Answer:
132 m
Step-by-step explanation:
Refer to attachment for figure.
In smaller triangle with angle theta , we have ,
⇒ tanθ = p/b
⇒ tanθ = h/121m
⇒ tanθ = h/121 m
<u>In</u><u> </u><u>triangle</u><u> </u><u>with</u><u> </u><u>angle </u><u>9</u><u>0</u><u>-</u><u>∅</u>
⇒ tan(90-θ) = p/b
⇒ cot θ = h/144 m
Multiplying these two ,
=> tanθ . cotθ = h/121 m × h/144m
=> 1 = h²/ (121 m × 144m )
=> h² = 121m × 144m
=> h= √ ( 121m × 144m)
=> h = 11m × 12m
=> h = 132 m
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We have to prove that rectangles are parallelograms with congruent Diagonals.
Solution:
1. ∠R=∠E=∠C=∠T=90°
2. ER= CT, EC ║RT
3. Diagonals E T and C R are drawn.
4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]
5. Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]
6. In Δ ERT and Δ CTR
(a) ER= CT→→[Opposite sides of parallelogram]
(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]
(c) Side TR is Common.
So, Δ ERT ≅ Δ CTR→→[SAS]
Diagonal ET= Diagonal CR →→→[CPCTC]
In step 6, while proving Δ E RT ≅ Δ CTR, we have used
(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]
Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.
