<h3>
Answer: 45</h3>
The value is approximate.
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Explanation:
Focus on the upper triangle.
Label the unknown horizontal side as y
Use the pythagorean theorem to solve for y
a^2+b^2 = c^2
10^2 + y^2 = 26^2
100+y^2 = 676
y^2 = 676-100
y^2 = 576
y = sqrt(576)
y = 24
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Now move to the bottom triangle
With respect to the reference angle, the side y = 24 is opposite this. The hypotenuse is unknown.
Use the sine rule to connect the two and solve for x
sin(angle) = opposite/hypotenuse
sin(32) = y/x
sin(32) = 24/x
x*sin(32) = 24
x = 24/sin(32)
x = 45.2899179551967 which is approximate
x = 45 rounding to the nearest whole number
Side x is approximately 45 cm long.
Note: make sure your calculator is in degree mode.
Answer:
120√2 m is the diameter of the path.
Step-by-step explanation:
We are given the following in the question:
When Luis has walked one-quarter of the distance around the circular path, the magnitude of his displacement is 120 m.
Displacement = 120 m
The two radius and the displacement forms a right angles triangle.
By Pythagoras theorem:
where r is the radius of the circular path.
Thus, diameter of circular path is
Thus, 120√2 m is the diameter of the path.
The attached image shows the circular path.
Answer:
- <u>Surface Area = 188.4 square yards</u>
- <u>Volume = 216 cubic yards</u>
Step-by-step explanation:
Finding the hypotenuse of the triangular side :
- Applying Pythagorean theorem
- √6² + 6²
- √2 x 6²
- 6√2
Finding Surface Area :
- Area (2 triangles) + Area (2 smaller rectangles) + Area (larger rectangle)
- 2 x 1/2 x 6 x 6 + 2 x 12 x 6 + 12 x 6√2
- 36 + 144 + 6√2
- 180 + 6√2
- 6 (30 + √2)
- 6 (30 + 1.4)
- 6 (31.4)
- <u>188.4 square yards</u>
<u></u>
Finding Volume :
- 1/2LWH
- 1/2 x 12 x 6 x 6
- 6³
- <u>216 cubic yards</u>
A. No
5 + 15 = 20
B. Yes
33/3 (33 ÷ 3) = 11
C. No
5 × 7 = 35
So firstly you are given the external angles, to find the internal angles, you do 180-133=47
180-142=38
the internal angles in a triangle add up to 180, therefore it is
47+38=85
180-85=95
because you have to find the external angle=n you then need to take 95 away from 180
180-95=85
so the answer is A
