Question

find ef.

triangle with right angle at f, angle at e is 25 degrees, hypotenuse ed is √62

write your answer as an integer or as a decimal rounded to the nearest tenth.
ef = blank
submit

Explanation:

Step1: Identify the triangle type and trigonometric ratio

We have a right - triangle \( \triangle EFD \) with \( \angle F = 90^{\circ} \), \( \angle E=25^{\circ} \) and hypotenuse \( ED=\sqrt{62} \). We want to find the length of \( EF \), which is the adjacent side to the angle \( \angle E \). The cosine of an angle in a right - triangle is defined as the ratio of the adjacent side to the hypotenuse. So, \( \cos(\angle E)=\frac{EF}{ED} \).

Step2: Substitute the known values and solve for \( EF \)

We know that \( \angle E = 25^{\circ} \) and \( ED=\sqrt{62}\approx7.874 \) (since \( \sqrt{64} = 8 \) and \( \sqrt{62}\approx7.874 \)). From the cosine formula \( \cos(25^{\circ})=\frac{EF}{ED} \), we can re - arrange it to get \( EF = ED\times\cos(25^{\circ}) \).

We know that \( \cos(25^{\circ})\approx0.9063 \) and \( ED = \sqrt{62}\approx7.874 \). Then \( EF=\sqrt{62}\times\cos(25^{\circ})\approx7.874\times0.9063 \).

First, calculate \( \sqrt{62}\approx7.874 \). Then \( 7.874\times0.9063\approx7.1 \)

Answer:

\( 7.1 \)