Domanda del libro di testo
In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.
v = 3i, w = -4i
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Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 4, Problema 29
In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit.
a = 11 yards, b = 9 yards, c = 7 yards
Guida verificata passo dopo passo1
Identify the side lengths of the triangle: \(a = 11\) yards, \(b = 9\) yards, and \(c = 7\) yards.
Calculate the semi-perimeter \(s\) of the triangle using the formula: \(s = \frac{a + b + c}{2}\).
Substitute the values of \(a\), \(b\), and \(c\) into the semi-perimeter formula to find \(s\).
Apply Heron's formula to find the area \(A\) of the triangle: \(A = \sqrt{s(s - a)(s - b)(s - c)}\).
Substitute the values of \(s\), \(a\), \(b\), and \(c\) into Heron's formula and simplify under the square root to find the area, then round to the nearest square unit.
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Heron's Formula
Heron's formula calculates the area of a triangle when the lengths of all three sides are known. It uses the semi-perimeter, s = (a + b + c) / 2, and the area is found by √[s(s - a)(s - b)(s - c)]. This method avoids needing the height or angles.
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Percorso guidato
6:36
Quadratic Formula
Semi-perimeter of a Triangle
The semi-perimeter is half the perimeter of a triangle, calculated as s = (a + b + c) / 2. It is a key intermediate value in Heron's formula, simplifying the area calculation by incorporating all three side lengths into one term.
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Percorso guidato
5:3530-60-90 Triangles
Rounding and Units in Measurement
After calculating the area, it is important to round the result to the nearest whole number as specified. Additionally, the units of the area are the square of the side length units (e.g., square yards), reflecting the two-dimensional nature of area.
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Percorso guidato
06:11Introduction to the Unit Circle
Pratica correlata
Domanda del libro di testo
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
-4w
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Domanda del libro di testo
In Exercises 23–32, use the dot product to determine whether v and w are orthogonal.
v = 3i, w = -4j
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Domanda del libro di testo
In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar.
||-2v||
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Domanda del libro di testo
In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar.
w - v
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Domanda del libro di testo
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.
a = 95, c = 125, A = 49°
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