Answer:
(a) α = 60°, β = 30°
(b) α ≈ 67.4°, β ≈ 22.6°
Step-by-step explanation:
I'll do (a) and (b) as examples. Make sure your calculator is set to degrees, not radians.
(a) For α, we're given the opposite and adjacent sides, so use tangent.
tangent = opposite / adjacent
tan α = √300 / 10
tan α = √3
α = 60°
Since angles of a triangle add up to 180°, we know that β = 30°. But we can use tangent again to prove it:
tan β = 10 / √300
tan β = 1 / √3
tan β = √3 / 3
β = 30°
(b) For α, we're given the adjacent side and the hypotenuse. So use cosine.
cos α = adjacent / hypotenuse
cos α = 15 / 39
cos α = 5 / 13
α ≈ 67.4°
Again, we know that β = 22.6°, but let's show it using trig. We're given the opposite side and hypotenuse, so use sine:
sin β = 15 / 39
sin β = 5 / 13
β ≈ 22.6°
Answer:
x = 15
Step-by-step explanation:
the opposite angle of a cyclic quadrilateral sum to 180° , then
6x + 20 + 3x + 25 = 180
9x + 45 = 180 ( subtract 45 from both sides )
9x = 135 ( divide both sides by 9 )
x = 15
the height of the poster must be multiplied by the ratio which is 1 to 2.5 which is 40 cm.
Step-by-step explanation:
sin 0 = opposite ÷ hypothenus
sin 0 = 3 / 5
3 / 5 = x / 15
5 × n = 15
n = 3
x = 3 × 3 = 9
y = use pythagoras
= 12
tan 0 = opposite ÷ adjacent
tan 0 = 9/12
The answer is the second option, option B, which is: B. <span>W'(2,8), X'(2,2), Y'(8,2)
</span> The explanation is shown below:
You have the Triangle WXY has coordinates W(1,4), X(1,1), and Y(4,1) and the Triangle of the option B has coordinates W'(2,8), X'(2,2), Y'(8,2). As you can notice, the coordinates of the new triangle are the result of multiply the coordinates of the original triangle by a scale of factor of 2. Therefore, in other words, the Triangle WXY was dilated with a scale of factor of 2.
