5) In the figure, triangle ABC is a right triangle at B. If CD = 15, find BC to the nearest tenth.
1 answer:
Answer:
BC ≈ 4.0
Step-by-step explanation:
∠ DCA = 180° - 70° = 110° ( adjacent angles )
∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle
∠ DAC = 180° - 140° = 40°
Using the Sine rule in Δ ACD to find common side AC
=
( cross- multiply )
AC × sin40° = 15 × sin30° ( divide both sides by sin40° )
AC = ≈ 11.668
Using the cosine ratio in right triangle ABC
cos70° = =
=
( multiply both sides by 11.668 )
11.668 × cos70° = BC , then
BC ≈ 4.0 ( to the nearest tenth )
You might be interested in
First, let's create the ratios of sweetened to unsweetened. To do this, you would have to subtract the number of people that preferred unsweetened from the total.
Westside mall: 15:30 or
Eastside mall: 13:26 or
Now, you would divide to both ratios.
15 ÷ 30 = 0.5
13 ÷ 26 = 0.5
They have the same sum, meaning, they are the same.
Westside Mall shoppers are just as likely to prefer unsweetened tea as Eastside Mall shoppers.
I hope this helps!
Westside mall: 15:30 or
Eastside mall: 13:26 or
Now, you would divide to both ratios.
15 ÷ 30 = 0.5
13 ÷ 26 = 0.5
They have the same sum, meaning, they are the same.
Westside Mall shoppers are just as likely to prefer unsweetened tea as Eastside Mall shoppers.
I hope this helps!
Answer:
A ≈ 25.1 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² ×
= π × 6² ×
= 36π ×
= 18 ×
= 2 × 4π
= 8π
≈ 25.1 cm² ( to the nearest tenth )