Part A)<span>In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
we know that </span>cos 45°=√2/2 [he length of the hypotenuse]=11/cos 45-----------> 11/(√2/2)----> (11*2)/√2 =22/√2-------> 11√2 in
the answer Part A) is 11√2 in
Part B) <span>What is the exact value of sin 45° ? </span> we know that sin 45°=11/(11√2)-------> 1/√2---------> (1/√2)*(√2/√2)-----> √2/2 the answer part b) is √2/2
Part C) <span>What is the area of a regular hexagon with a side length of 4 m?
we know that
</span>In case of a regular hexagon <span> each of the six triangles that are formed by connecting its center with all six vertices is an equilateral triangle with a side equaled to 4 m. The area of this hexagon is six times greater than the area of such a triangle </span> In an equilateral triangle with a side d<span> the altitude </span>h can be calculate from the Pythagorean Theorem as h²=d²−(d/2)²=(3/4)d² <span>Therefore, </span><span>h=d<span>√3/2
</span></span><span>Area of such a triangle is </span>A=d*h/2------------> d²*√3/4 From this the area of the regular hexagon with a side d<span> is </span>S=6*A----------> d²3√3/2 for d=4 m S=4²3√3/2------> 24√3 m²------------> 41.57 m²
the answer Part C) is 41.57 m²
Part D) <span>In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm? </span>[he length of the hypotenuse]=5/sin 30--------> 5/(1/2)---------> 10 cm
