Ashooting star forms a right triangle with the earth and the sun, as shown below: a right triangle is shown with the vertices labeled earth, sun, and shooting star. the angle formed by the sun is labeled x degrees and the side between the earth and the sun is labeled y. a scientist measures the angle x and the distance y between the earth and the sun. using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the earth and the shooting star.

Step-by-step explanation:

The scientist can use only the angle x and the distance y to calculate the distance between the Earth and the Sun using the cosine function.The cosine of an angle is equal to the ratio of the length of the adjacent side and the length of the hypotenuse. In equation form:cos x = BC / ySolving for BCBC = y cos xBC is the distance between the Earth and the Sun

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

i think the length is 12 and the width is 17