Triangle LMN is inscribed inside a circle with diameter LM and the inscribed angle at N. The length of LM is 22 cm and the length of MN is 7 cm. Using what you know about inscribed angles, find the approximate angle measure of L.(1 point)

Question

Responses

19°
19°

71°
71°

90°
90°

38°

Answer 1

To find the measure of angle L in triangle LMN inscribed in a circle with diameter LM, we can use the properties of inscribed angles.

Since LM is the diameter of the circle, the triangle LNM forms a right triangle with angle N being the right angle (90°) due to the inscribed angle theorem.

Given:

• LM is the diameter = 22 cm.
• MN is the length = 7 cm.

To find the angle L, we can use the sine definition in triangle LNM:

Since we have:

1. LM (the hypotenuse) = 22 cm
2. MN (the opposite side to angle L) = 7 cm

Using the sine function:

\[ \sin(L) = \frac{opposite}{hypotenuse} = \frac{MN}{LM} = \frac{7}{22} \]

Now, we calculate angle L:

\[ L = \arcsin\left(\frac{7}{22}\right) \]

Using a calculator:

\[ L \approx 18.8° \]

Rounding to the nearest degree, angle L is approximately 19°.

Thus, the answer is:

19°