The diagram shows some straight line distances between Auckland (A), Hamilton (H), Tauranga (7)
and Rotorua (R).
AT=180 km, AH=115 km and HT= 90 km.
(a) Calculate angle HAT.
Show that this rounds to 25.0°, correct to 3 significant figures.
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Given : diagram showing some straight line distances between Auckland (A), Hamilton (H), Tauranga (T) and Rotorua (R).
AT=180 km, AH=115 km and HT= 90 km.
To find : angle HAT
Step-by-step explanation:
Let say ∠ HAT = α
Applying triangle cosine formula
90² = 115² + 180² - 2(115)(180)Cosα
=> 18² = 23² + 36² - 2(23)(36)Cosα
=> 324 = 529 + 1296 - 1656Cosα
=> -1501 = - 1656Cosα
=> Cosα = 1501/1656
=> Cosα = 0.9064
=> α = 24.987
=> α = 25°
=> ∠ HAT = 25°
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Answer:
25
Step-by-step explanation:
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