The figure shows a square, a regular pentagon and a regular hexagon put together. What is the measure of ∠BAC
1 answer:
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Answer:
see explanation
Step-by-step explanation:
(a)
Sum the parts of the ratio , 1 + 2 + 3 = 6 parts
Divide sum of angles in a triangle by 6 to find the value of one part of the ratio.
180° ÷ 6 = 30° ← value of 1 part of the ratio
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Since there is an angle of 90° then the triangle is right.
(b)
The shortest side is the side opposite the smallest angle of 30°
Using the sine ratio and the exact value
sin30° = , then
sin30° = =
=
( cross- multiply )
2 opp = 19 ( divide both sides by 2 )
opp = 9,5
Shortest side in the triangle is 9.5 cm