Let x = the length of the triangle's hypotenuse
using proportions, this is what the equation looks like:
cross multiply to get:
divide both sides by 45 to get
x=12
Answer:
c squared
Step-by-step explanation:
Answer:
The ratio 1:3:5 by doubling each number is the same as 2:6:10 and the big one 10 is 10/(2+6+10) = 10/18 of the total, so multiplying top and bottom by 10 gives 100/180, so the biggest angle is 100° since the sum of all angles must be 180°.
Answer: a. 90°
Step-by-step explanation:
We know that the in a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.
In the problem∠XYZ is the inscribed angle
∠XYZ=![\frac{1}{2}\ arc(XZ)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5C%20arc%28XZ%29)
⇒ ∠XYZ=![\frac{1}{2}\angle{XZ}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cangle%7BXZ%7D)
Since XZ is a diameter of the circle which is a line segment, thus ∠XZ=180°
∴ ∠XYZ=![\frac{1}{2}180^{\circ}=90^{\circ}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D180%5E%7B%5Ccirc%7D%3D90%5E%7B%5Ccirc%7D)
∴ ∠XYZ=![90^{\circ}](https://tex.z-dn.net/?f=90%5E%7B%5Ccirc%7D)
Therefore, a. 90° is the measure of ∠XYZ.
Answer:
Explanation:
The distance traveled by June, from A to D, is the sum of the distance from A to C plus the distance from C to D:
- Travel from A to D = Distance AC + Distance DC.
<u>1) Find the distance AC</u>
- Triangle ABC is a right triangle, from which you have to calculate the hypotenuse (AC), knowing angle A (50º), and its adjacent leg (217 m).
- AC = 217m / cos (50º) = 337.59m
<u>2) Find the distance DC</u>
First, you need to calculate the side BC which is a common side of both triangles ABC and DBC.
You can use Pythagora's or a trigonometric function (tangent or sine).
- tan (50º) = BC / 217 m ⇒ BC = 217 m × tan (50º) = 258.61 m
Now you can use Pythagora's theorem to find the distance DC, which is the hypotenuse of the triangle DBC:
- DC² = (170m)² + (258.62)² = 95,779.41m²
<u>3) Find the total distance traveled from A to D</u>
- Travel from A to D = Distance AC + Distance DC = 337.59m + 309.48m = 647.07 m ≈ 647m.