Answer:
m∠x = 10°
Step-by-step explanation:
Since we are dealing with a <u>right triangle</u> and its two sides and one angle, we can use <u>trigonometry ratios</u>. Remember them all with the acronym SohCahToa.
"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.
The ratios are:
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.
In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.
sinθ = opposite/hypotenuse
sinx = CB/AB Substitute the labels in the diagram
sinx = 4/23 Substitute known values (side lengths)
x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.
x = 10.015....° Exact answer
x ≈ 10° Round to the nearest degree
Therefore the measure of angle x (m∠x) is 10°.
Answer:
120 people
Step-by-step explanation:
Length of dance floor = 30 ft
Width of dance floor = 20 ft
Given that 2 people will occupy 5 ft² of space, the number of people that will crowd the floor of the dance floor is calculated as follows:
= Area of dance floor ÷ 5 ft²
= (30*20) ÷ 5
= 600 ÷ 5
= 120.
120 people will crowd the dance floor.
Answer:
D. 4,704 ft²
Step-by-step explanation:
Giving a scale of 1 in. = 14 ft, to find the actual area of the field represented by the triangular drawing above, convert the length of the base and height to the actual lengths of the field using the scale.
Height of drawing = 8 in.
Actual height = 8*14 = 112 ft
Base of drawing = 6 in.
Actual base = 6*14 = 84 ft
Area of the field = area of ∆
Area = ½*base*height
Area = ½*84*112
Area = 4,704 ft²
Answer:
63
Step-by-step explanation:
the numbers are in ratio 7 : 9 = 7x : 9x ( x is a multiplier )
given the sum of the numbers = 112 , then
7x + 9x = 112 , that is
16x = 112 ( divide both sides by 16 )
x = 7 , then
9x = 9 × 7 = 63 ← value of larger number
Answer:
(4,3)
Step-by-step explanation:
To find the midpoint add the end points and divide by 2
P(2,5) S ( sx, sy) and the midpoint is and H (3,4)
X coordinate
( 2+ sx) /2 = 3
Multiply each side by 2
2+sx = 3*2
2+sx = 6
Subtract 2
sx = 4
Y coordinate
( 5+ sy) /2 = 4
Multiply each side by 2
5+sy = 4*2
5+sy = 8
Subtract 5
sy = 3
The end point is
(4,3)
