7)
The internal angles of a triangle must add up to 180.
The given answer is 64º and we can verify that:
Then, the answer is correct.
Notice that the measurement of 26.0º has three significant figures while the 90º angle is an exact value. Then, the answer must have 3 significant figures too: 64.0º.
8)
The tangent of an angle in a right triangle is the quotient between the side opposite to it and the side adjacent to it.
The tangent of 26º is 0.4877, and the quotient of the lengths of the sides according to the answer, is:
![\frac{8.00\operatorname{cm}}{16.4\operatorname{cm}}=0.488\ldots]()
The length of 16.4cm has the correct number of significant figures and matches the value of the tangent. Then, the answer is correct.
9)
Using the Pythagorean Theorem, we should verify that:
![\begin{gathered} (18.3\operatorname{cm})^2=(8.00\operatorname{cm})^2+(16.4\operatorname{cm})^2 \\ \Rightarrow335cm^2=64.0\operatorname{cm}+269\operatorname{cm} \\ \Rightarrow335\operatorname{cm}^2=333\operatorname{cm} \end{gathered}]()
To be precise, if the length of the hypotenuse is calculated, the result is 18.249...cm, so it should be rounded down to 18.2cm.