In the ABC triangle it is known:
Angle C is 90 °;
angle A = 30 °;
Hypotenuse AB = √3.
Let’s find the AC.
The cosine of angle A is equal to the ratio of the adjacent leg to the hypotenuse.
AC is the adjacent leg in relation to angle A.
AB – hypotenuse.
Since the hypotenuse and angle are known, then we can find the AC leg.
We get the formula in the form:
cos a = AC / AB;
Let us express from the formula AC.
AC = AB * cos a;
Substitute the known values and calculate the AC.
AC = √3 * cos 30 ° = √3 * 1/2 = √3 / 2;
As a result, we got that the leg of the triangle ABC is equal to AC = √3 / 2.
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