The sides of an isosceles triangle are 5, 5, and 7. Find the measure of the vertex angle to the nearest degree.

2 answers:

8 0

You can use the cosine law with the formula:
a^2 = b^2 + c^2 - 2*b*c*cosA
With a = 5, b = 5, c = 7,
7^2 = 5^2 + 5^2 - 2*5*7*cosA
49 = 25 + 25 - 70*cosA
70*cosA = 25 + 25 - 49
70*cosA = 1
cosA = 1/70
A = arccos (1/70) = 89.18 deg = 89 deg

olga2289 [7]3 years ago

7 0

Answerino:

89 degrees

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The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0) . The focus of the reflector

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Answer:

The depth of the reflector is 0.84 feet

Step-by-step explanation:

<em>(See the figure below)</em>

The equation of a parabola centered at the origin with an axis of symmetry on y-axis is:

$x^{2}=4py$ (1)

With p the distance from the origin to the focus using p=6, the equation (1) of the parabola becomes:

$x^{2}=4(6)y=24y$ (2)

Note that the point B is on the parabola, so this point should satisfy the parabola equation (2) that allow us to use the value x=4.5 to find the y value associated to it, that it is the depth (h) of the reflector:

$(4.5)^{2}=24y$ , solving for y