Answer:
a = 
b = 12
c = 
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths 
.
A 30-60-90 right triangle has side lengths 
.
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length 
. Therefore, 
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to 
. This means was multiplied by 
. This means that side c is 
.
Answer: There are 20 boys
Step-by-step explanation:
Any smooth curve connecting two points is called an arc. The length of the arc m∠QPR is 2.8334π m.
<h3>What is the Length of an Arc?</h3>
Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
where
θ is the angle, that which arc creates at the centre of the circle in degree.
Given the radius of the circle is 3m, while the angle made by the arc at the centre of the circle is 170°. Therefore,
The length of an arc = 2πr×(θ/360°) = 2π × 3 ×(170/360°) = 2.8334π m
Hence, the length of the arc m∠QPR is 2.8334π m.
Learn more about Length of an Arc:
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Answer: 118
Explanation:
Since ∠A=∠ADB: ∠ADB=61°. The sum of the interior angles of any triangle is 180°, thus:
61°+61°= 122
180-122=58°
∠DBA=58°
Since triangle BCD is an equilateral triangle, all the interior angles are the same:
180/3=60
∠DBC=60°
∠BCD=60°
∠CDB=60°
Since angles DBC and DBA make up angle ABC, just simply add the two angles together:
58+60=118°
Therefore, ∠ABC is 118°.
