Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a fl
agpole, as shown below:
Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole. Angle ADC measures 45 degrees, and angle BDC measures 30 degrees. The length of DC is 5 multiplied by square root of 3.
Angle ADC measures 45°, and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?
Two ropes, AD and BD, are tied to a peg on the ground at point D. The other ends of the ropes are tied to points A and B on a flagpole. Angle ADC measures 45 degrees, and angle BDC measures 30 degrees. The length of DC is 5 multiplied by square root of 3.
Angle ADC measures 45°, and angle BDC measures 30°. What is the distance between the points A and B on the flagpole?
1 answer:
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Answer:
AB ≈ 15.7 cm, BC ≈ 18.7 cm
Step-by-step explanation:
(1)
Using the Cosine rule in Δ ABD
AB² = 12.4² + 16.5² - (2 × 12.4 × 16.5 × cos64° )
= 153.76 + 272.25 - (409.2 cos64° )
= 426.01 - 179.38
= 246.63 ( take the square root of both sides )
AB = ≈ 15.7 cm ( to 1 dec. place )
(2)
Calculate ∠ BCD in Δ BCD
∠ BCD = 180° - (53 + 95)° ← angle sum in triangle
∠ BCD = 180° - 148° = 32°
Using the Sine rule in Δ BCD
=
=
( cross- multiply )
BC × sin32° = 12.4 × sin53° ( divide both sides by sin32° )
BC = ≈ 18.7 cm ( to 1 dec. place )
