Find the measure of the indicated angle to the nearest degree
1 answer:
Answer:
A) 18°
Step-by-step explanation:
To find the measure of the indicated angle, we can use trigonometric ratios.
Looking at the triangle, we can see that we are given the lengths of the two legs of the triangle, but not the hypotenuse. Since we are not given the hypotenuse, the sine and cosine ratios would not work since both of them require the length of the hypotenuse. We can use the tangent ratio, since it only requires the lengths of the two legs. Remember:
From looking at the image, we can see that the length of the side opposite to the angle is 3, and the length of the side adjacent to the angle is 9. Thus, we can use 3 as out opposite and 9 as out adjacent:
Now we solve for ?. Lets take the inverse tan of both sides to get rid of the tan on the left side:
And we get:
? ≈ 18.4349488° ≈ 18°
So the answer would be 18°, or A.
I hope you find my answer to be helpful. Happy studying.
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Answer:
(3, 1.7)
Step-by-step explanation:
The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.
Two lines are perpendicular if the product of their slopes is -1.
The slope of the line joining D(0,0), F(3,7) is:
The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:
The slope of the line joining E(7,0), and F(3,7). is:
The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:
The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:
x = 3, y = 1.7