The angle between perpendicular and oblique is 45 °. Find the distance from the point to the plane and the value of the inclined, if the length of the projection of the straight line onto the plane is 25 cm.
Given: AB is a perpendicular dropped on plane a. AC – oblique. BC = 25 cm. BAC angle = 45 °
Find: AB- ?, AC-?
Solution: ABC = 90 °, since AB is perpendicular to plane a. Hence, triangle ABC is rectangular. The sum of the acute angles in a right-angled triangle is 90 °, that is, BAC + ACB = 90
BAC = 45, therefore ACB = 90-45 = 45. We got that 2 angles in a triangle (BAC and ACB) are equal. Then, on the basis of an isosceles triangle, this triangle is isosceles. Hence, BC = AB, AB = 25 cm.
Next, we apply the Pythagorean theorem:
AC ^ 2 = AB ^ 2 + BC ^ 2
AC ^ 2 = 25 ^ 2 + 25 ^ 2
AC ^ 2 = 2 * 25 ^ 2
AC = 25 * √2
Answer: AB = 25, AC = 25 * √2
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