What is the length of the missing side AB?

72.6 cm

Step-by-step explanation:

Since we know the two sides and one angle, we would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and C is the angle corresponding to AB.

AB² = 38² + 83² - 2(38 × 83)Cos61

AB² = 1444 + 6889 - 2(3154)0.4848

AB² = 8333 - 3058.1184

AB² = 5274.8816

Taking square root of both sides, it becomes

AB = √5274.8816

AB = 72.6 rounded up to the nearest tenth

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.