Question

1. a) classify (name) the triangle by angle and sides.

b) what is the shortest side?
c) what is the longest side?
d) legs
e) hypotenuse
(image of a right triangle with right angle at n, side fn = 5, side fu = 10, angle at u is 30°)

Explanation:

a)

Step1: Classify by angle

The triangle has a right angle (at \( N \)), so by angle, it is a Right triangle.

Step2: Classify by sides

The side lengths are \( 5 \), \( 10 \), and the length of \( UN \) (we can calculate \( UN \) using Pythagoras: \( UN = \sqrt{10^2 - 5^2} = \sqrt{100 - 25} = \sqrt{75} \approx 8.66 \)). Since all three sides (\( 5 \), \( \approx 8.66 \), \( 10 \)) have different lengths, by sides, it is a Scalene triangle.

b)

Step1: Identify side lengths

The given side lengths (or visible sides) are \( 5 \) (side \( FN \)), \( 10 \) (side \( FU \)), and \( UN \approx 8.66 \) (calculated above).

Step2: Compare lengths

Among \( 5 \), \( 8.66 \), and \( 10 \), the smallest length is \( 5 \). So the shortest side is \( 5 \) (side \( FN \)).

c)

Step1: Identify side lengths

The side lengths are \( 5 \) ( \( FN \) ), \( \approx 8.66 \) ( \( UN \) ), and \( 10 \) ( \( FU \) ).

Step2: Compare lengths

Among \( 5 \), \( 8.66 \), and \( 10 \), the largest length is \( 10 \). So the longest side is \( 10 \) (side \( FU \)).

d)

Answer:

Right, Scalene (by angle: Right triangle; by sides: Scalene triangle)