Unit 7 Right Triangles And Trigonometry Homework 2 Answer Key (2024)

FAQs

How do you find the answer to a right triangle? ›

The Pythagorean Theorem gives us a² + b² = c² for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b² = 14² – 5² = 171. Therefore b is equal to the square root of 171 or approximately 13.07.

A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long.

In order to find the hypotenuse of a special right triangle 45-45-90, we can use the formula or ratio that is defined for its sides. We know that in this kind of triangle, Leg : Leg: Hypotenuse = x: x: x√2. Therefore, if we know the sides we can substitute the given values and calculate the length of the hypotenuse.

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides.

Solving right triangles

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a² + b² = c². Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

The 3-4-5 triangle is the simplest Pythagorean Triple because it has the smallest whole number side lengths. The 3-4-5 triangle rule states when the ratio 3:4:5 is present as the side lengths of a triangle, the triangle is a right triangle.

The hypotenuse is termed as the longest side of a right-angled triangle. To find the longest side we use the hypotenuse formula that can be easily driven from the Pythagoras theorem, (Hypotenuse)² = (Base)² + (Altitude)². Hypotenuse formula = √((base)² + (height)²) (or) c = √(a² + b²).

If you know the hypotenuse and the opposite side of the angle, you would use the sine function. If you know the hypotenuse and the adjacent side (next to) the angle, you would use the cosine function. If you know the opposite and adjacent sides to the angle, you use the tangent function.

SOHCAHTOA is a mnemonic device helpful for remembering what ratio goes with which function. SOH = Sine is Opposite over Hypotenuse. CAH = Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.

sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side. sec θ = Hypotenuse/Adjacent Side.

What is the rule for a right triangle? ›

The Pythagorean Theorem states that: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

A right triangle is a triangle with one 90 degree angle. The Pythagorean Theorem tells us that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. In formula form, it is a^2 + b^2 = c^2, where a and b are the two sides of the right triangle and c is the hypotenuse.

Sum of all sides of a triangle is called perimeter. If lengths of sides of a triangle are a,b and c then perimeter is P=a+b+c. Suppose P,a and b are given,use c=P-(a+b) to get length of third side.