Answer:
yesyes
Step-by-step explanation:
m GH = 57''
________
tan 39° = opposite / adjacent
tan 39° = m GH / m HJ
tan 39° * m HJ = m GH
m HJ = m GH / tan 39°
m HJ ≈ 57'' / 0.810
m HJ ≈ 70.4'' <——<span>— measure of the segment HJ</span>
________
sin 39° = opposite / hypotenuse
sin 39° = m GH / m GJ
sin 39° * m GJ = m GH
m GJ = m GH / sin 39°
m GJ = 57'' / 0.629
m GJ ≈ 90.6'' <——— measure of the segment GJ
________
So the perimeter is
p = m GH + m HJ + m GJ
p = 57'' + 70.4'' + 90.6''
p = 218'' <——<span>— this is the answer.</span>
I hope this helps. =)
Tags: <em>perimeter right triangle sine cosine tangent sin cos tan trig trigonometry geometry</em>
Answer:
∠1 = 50°
∠2 = ∠3 = 130°
Step-by-step explanation:
In an isosceles trapezoid, such as this one, the angles at either end of a base are congruent:
∠1 ≅ 50°
∠2 ≅ ∠3
The theorems applicable to transversals and parallel lines also apply to the sides joining the parallel bases. In particular, "consecutive interior angles are supplementary." That is, angles 1 and 2 are supplementary, for example.
∠2 = 180° -∠1 = 180° -50° = 130°
We already know angle 3 is congruent to this.
∠1 = 50°
∠2 = ∠3 = 130°
_____
<em>Additional comment</em>
It can be easier to see the congruence of the base angles if you remove the length of the shorter base from both bases. This collapses the figure to an isosceles triangle and makes it obvious that the base angles are congruent.
Alternatively, you can drop an altitude to the longer base from each end of the shorter base. That will create two congruent right triangles at either end of the figure. Those will have congruent corresponding angles.
The value of x would be: 5
1/9 = 2/18 = 3/27 = 4/36 = 5/45 = ... = n/(9n) for any n
