# Math Help - urgent help! :)

1. ## urgent help! :)

question-

Q1- Calculate the number of sides of a regular polygon whose interior angles are each 150degrees.

Q2- Find the height of a rectangular box of length 8cm, width 6cm where the length of diagnol is 11cm.

Q3- An aircraft flies equal distance South-East and then South-West to finish 120km due South of its starting point. How long is each part of its journey.

Q4- A cone has base radius 5cm and slant height 11cm. Find the vertical height.

2. Originally Posted by afreem
question-

Q1- Calculate the number of sides of a regular polygon whose interior angles are each 150degrees.
The central angle of one of the isosceles triangles which build a regular polygon is $\alpha = 180^\circ-(\text{interior angle})$. Thenumber of vertices is $n = \dfrac{360^\circ}{\alpha}$

Q2- Find the height of a rectangular box of length 8cm, width 6cm where the length of diagnol is 11cm.
The diagonal in a rectangular box with the edges a, b and c is

$D=\sqrt{a^2+b^2+c^2}$

Q3- An aircraft flies equal distance South-East and then South-West to finish 120km due South of its starting point. How long is each part of its journey.
You are dealing with an isosceles right triangle where the hypotenuse is 120 km long. Calculate the length of the legs.

Q4- A cone has base radius 5cm and slant height 11cm. Find the vertical height.
Height h, radius r and slant height s of a cone form a right triangle such that

$s^2 = r^2+h^2$